128:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000 Funciones racionales y cónicas:@0.073089:0.043661:0.343993:0.043661:0.343993:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 6.1 Hipérbola:@0.293660:0.240028:0.395441:0.240028:0.395441:0.223359:0.293660:0.223359:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Definición:@0.293660:0.267390:0.371630:0.267390:0.371630:0.250721:0.293660:0.250721:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Sean , , , tal que 0 y ,:@0.371523:0.267390:0.740178:0.267391:0.740178:0.251679:0.371523:0.251677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b c:@0.418001:0.267390:0.458166:0.267390:0.458166:0.251955:0.418001:0.251955:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.462071:0.267101:0.476708:0.267101:0.476708:0.253692:0.462071:0.253692:0.000000 R:@0.480577:0.266532:0.493867:0.266532:0.493867:0.253634:0.480577:0.253634:0.000000 2:@0.493769:0.261328:0.499006:0.261328:0.499006:0.252167:0.493769:0.252167:0.000000 ,:@0.572928:0.266572:0.586868:0.266572:0.586868:0.254103:0.572928:0.254103:0.000000 a:@0.590741:0.267391:0.600000:0.267391:0.600000:0.251956:0.590741:0.251956:0.000000 ,:@0.603878:0.266572:0.617817:0.266572:0.617817:0.254103:0.603878:0.254103:0.000000 c:@0.621691:0.267391:0.629348:0.267391:0.629348:0.251956:0.621691:0.251956:0.000000 b:@0.649136:0.267391:0.658395:0.267391:0.658395:0.251956:0.649136:0.251956:0.000000 2:@0.658336:0.261328:0.663573:0.261328:0.663573:0.252167:0.658336:0.252167:0.000000 5:@0.667485:0.266837:0.682818:0.266837:0.682818:0.253121:0.667485:0.253121:0.000000 c:@0.686683:0.267391:0.694341:0.267391:0.694341:0.251956:0.686683:0.251956:0.000000 2:@0.694261:0.261328:0.699497:0.261328:0.699497:0.252167:0.694261:0.252167:0.000000 2:@0.703407:0.266837:0.718741:0.266837:0.718741:0.253121:0.703407:0.253121:0.000000 a:@0.722606:0.267391:0.731865:0.267391:0.731865:0.251956:0.722606:0.251956:0.000000 2:@0.731785:0.261328:0.737021:0.261328:0.737021:0.252167:0.731785:0.252167:0.000000 1:@0.302022:0.297927:0.307259:0.297927:0.307259:0.288766:0.302022:0.288766:0.000000 (:@0.307270:0.294755:0.336593:0.294755:0.336593:0.279042:0.307270:0.279042:0.000000:0.000000:0.000000:0.000000 5 2:@0.311816:0.294200:0.351926:0.294200:0.351926:0.280484:0.311816:0.280484:0.000000:0.000000:0.000000 c:@0.351963:0.294755:0.359620:0.294755:0.359620:0.279319:0.351963:0.279319:0.000000 , 0), :@0.359638:0.294755:0.388556:0.294755:0.388556:0.279042:0.359638:0.279042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.401937:0.297927:0.407173:0.297927:0.407173:0.288766:0.401937:0.288766:0.000000 ( , 0). Se le llama hipérbola de eje principal al eje , y focos y , al :@0.407184:0.294755:0.930951:0.294755:0.930951:0.279042:0.407184:0.279042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.411731:0.294200:0.427064:0.294200:0.427064:0.280484:0.411731:0.280484:0.000000 c:@0.435973:0.294755:0.443631:0.294755:0.443631:0.279319:0.435973:0.279319:0.000000 x:@0.784073:0.294755:0.791528:0.294755:0.791528:0.279319:0.784073:0.279319:0.000000 1:@0.866469:0.297927:0.871706:0.297927:0.871706:0.288766:0.866469:0.288766:0.000000 2:@0.901812:0.297927:0.907049:0.297927:0.907049:0.288766:0.901812:0.288766:0.000000 conjunto de puntos del plano definido y denotado como::@0.293657:0.311396:0.702708:0.311396:0.702708:0.295684:0.293657:0.295684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( , , ) | :@0.442100:0.338760:0.630707:0.338760:0.630707:0.323047:0.442100:0.323047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.461379:0.338760:0.486891:0.338760:0.486891:0.323324:0.461379:0.323324:0.000000:0.000000:0.000000 5:@0.495561:0.338205:0.510894:0.338205:0.510894:0.324489:0.495561:0.324489:0.000000 [:@0.535043:0.338470:0.549679:0.338470:0.549679:0.325060:0.535043:0.325060:0.000000 R:@0.553549:0.337900:0.566839:0.337900:0.566839:0.325002:0.553549:0.325002:0.000000 2:@0.566740:0.332696:0.571977:0.332696:0.571977:0.323535:0.566740:0.323535:0.000000 | ||:@0.583651:0.339453:0.599155:0.339453:0.599155:0.320598:0.583651:0.320598:0.000000:0.000000:0.000000:0.000000 2:@0.611435:0.338205:0.626768:0.338205:0.626768:0.324489:0.611435:0.324489:0.000000 1:@0.638908:0.341932:0.644145:0.341932:0.644145:0.332772:0.638908:0.332772:0.000000 ||:@0.644099:0.339453:0.651830:0.339453:0.651830:0.320598:0.644099:0.320598:0.000000:0.000000 :@0.651741:0.338760:0.714167:0.338760:0.714167:0.323047:0.651741:0.323047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.655699:0.338205:0.671032:0.338205:0.671032:0.324489:0.655699:0.324489:0.000000 ||:@0.674883:0.339453:0.682614:0.339453:0.682614:0.320598:0.674883:0.320598:0.000000:0.000000 2:@0.694895:0.338205:0.710228:0.338205:0.710228:0.324489:0.694895:0.324489:0.000000 2:@0.722368:0.341932:0.727605:0.341932:0.727605:0.332772:0.722368:0.332772:0.000000 || |:@0.727558:0.339453:0.743075:0.339453:0.743075:0.320598:0.727558:0.320598:0.000000:0.000000:0.000000:0.000000 2 .:@0.742973:0.338760:0.795323:0.338760:0.795323:0.323047:0.742973:0.323047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.746930:0.338205:0.762264:0.338205:0.762264:0.324489:0.746930:0.324489:0.000000 a:@0.775020:0.338760:0.784279:0.338760:0.784279:0.323324:0.775020:0.323324:0.000000 Claramente, ( , , ) .:@0.293652:0.366122:0.495760:0.366123:0.495760:0.350410:0.293652:0.350409:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.420774:0.366123:0.446286:0.366123:0.446286:0.350688:0.420774:0.350688:0.000000:0.000000:0.000000 [:@0.454956:0.365984:0.470289:0.365984:0.470289:0.351936:0.454956:0.351936:0.000000 R:@0.474155:0.365263:0.487445:0.365263:0.487445:0.352366:0.474155:0.352366:0.000000 2:@0.487368:0.360059:0.492605:0.360059:0.492605:0.350898:0.487368:0.350898:0.000000 En muchos libros de geometría analítica, se define la hipérbola como el conjunto de :@0.293667:0.393485:0.931486:0.393485:0.931486:0.377772:0.293667:0.377772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 puntos del plano, tal que el valor absoluto de las diferencias de las distancias de a :@0.293667:0.410127:0.913247:0.410128:0.913247:0.394415:0.293667:0.394414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.921674:0.411409:0.926911:0.411409:0.926911:0.402249:0.921674:0.402249:0.000000 y a es una constante dada. La distancia del punto a es || || y la distancia del :@0.293660:0.426770:0.931036:0.426770:0.931036:0.411057:0.293660:0.411057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.337434:0.428681:0.342671:0.428681:0.342671:0.419521:0.337434:0.419521:0.000000 1:@0.710615:0.429942:0.715851:0.429942:0.715851:0.420782:0.710615:0.420782:0.000000 2:@0.761870:0.426215:0.777204:0.426215:0.777204:0.412499:0.761870:0.412499:0.000000 1:@0.788988:0.429942:0.794224:0.429942:0.794224:0.420782:0.788988:0.420782:0.000000 punto a es || ||, con lo que la hipérbola es el conjunto de puntos del plano, tal :@0.293667:0.443412:0.931013:0.443412:0.931013:0.427699:0.293667:0.427699:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.374476:0.446584:0.379713:0.446584:0.379713:0.437423:0.374476:0.437423:0.000000 2:@0.422432:0.442857:0.437765:0.442857:0.437765:0.429141:0.422432:0.429141:0.000000 2:@0.449647:0.446584:0.454883:0.446584:0.454883:0.437423:0.449647:0.437423:0.000000 que || || || || es una constante dada, la cual se ha elegido como 2 .:@0.293660:0.460053:0.866839:0.460053:0.866839:0.444341:0.293660:0.444341:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.346057:0.459499:0.361390:0.459499:0.361390:0.445783:0.346057:0.445783:0.000000 1:@0.373531:0.463226:0.378768:0.463226:0.378768:0.454065:0.373531:0.454065:0.000000 2:@0.390317:0.459499:0.405650:0.459499:0.405650:0.445783:0.390317:0.445783:0.000000 2:@0.433467:0.459499:0.448800:0.459499:0.448800:0.445783:0.433467:0.445783:0.000000 2:@0.460940:0.463226:0.466177:0.463226:0.466177:0.454065:0.460940:0.454065:0.000000 a:@0.854450:0.460053:0.863709:0.460053:0.863709:0.444618:0.854450:0.444618:0.000000 De la definición de hipérbola, esto es, del conjunto :@0.293655:0.487415:0.676423:0.487415:0.676423:0.471703:0.293655:0.471703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( , , ), se tienen las siguientes :@0.695337:0.487417:0.931072:0.487417:0.931072:0.471704:0.695337:0.471704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.715772:0.487417:0.742297:0.487417:0.742297:0.471981:0.715772:0.471981:0.000000:0.000000:0.000000 equivalencias: :@0.293657:0.504058:0.399112:0.504058:0.399112:0.488346:0.293657:0.488346:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.305290:0.531132:0.319926:0.531132:0.319926:0.517722:0.305290:0.517722:0.000000 ( , , ) :@0.319839:0.531422:0.395698:0.531422:0.395698:0.515709:0.319839:0.515709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.361424:0.531422:0.386936:0.531422:0.386936:0.515986:0.361424:0.515986:0.000000:0.000000:0.000000 :@0.411386:0.531422:0.415289:0.531422:0.415289:0.514752:0.411386:0.514752:0.000000 | || || || || | 2 ,:@0.415210:0.531422:0.618958:0.531422:0.618958:0.515709:0.415210:0.515709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.442991:0.530867:0.458325:0.530867:0.458325:0.517151:0.442991:0.517151:0.000000 1:@0.470467:0.534594:0.475704:0.534594:0.475704:0.525434:0.470467:0.525434:0.000000 2:@0.487253:0.530867:0.502586:0.530867:0.502586:0.517151:0.487253:0.517151:0.000000 2:@0.526452:0.530867:0.541785:0.530867:0.541785:0.517151:0.526452:0.517151:0.000000 2:@0.553925:0.534594:0.559162:0.534594:0.559162:0.525434:0.553925:0.525434:0.000000 5:@0.578481:0.530867:0.593814:0.530867:0.593814:0.517151:0.578481:0.517151:0.000000 a:@0.606570:0.531422:0.615829:0.531422:0.615829:0.515986:0.606570:0.515986:0.000000 ( , , ) | || || || || | ≠ 2 .:@0.302077:0.551638:0.614740:0.551638:0.614740:0.535925:0.302077:0.535925:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ó:@0.305290:0.551348:0.319926:0.551348:0.319926:0.537938:0.305290:0.537938:0.000000 a b:@0.361424:0.551638:0.386936:0.551638:0.386936:0.536202:0.361424:0.536202:0.000000:0.000000:0.000000 2:@0.443119:0.551083:0.458452:0.551083:0.458452:0.537367:0.443119:0.537367:0.000000 1:@0.470592:0.554810:0.475829:0.554810:0.475829:0.545650:0.470592:0.545650:0.000000 2:@0.487378:0.551083:0.502711:0.551083:0.502711:0.537367:0.487378:0.537367:0.000000 2:@0.526579:0.551083:0.541912:0.551083:0.541912:0.537367:0.526579:0.537367:0.000000 2:@0.554052:0.554810:0.559289:0.554810:0.559289:0.545650:0.554052:0.545650:0.000000 a:@0.602351:0.551638:0.611610:0.551638:0.611610:0.536202:0.602351:0.536202:0.000000 Sea ( , ) . La distancia de a está definida como::@0.293662:0.579000:0.729244:0.579001:0.729244:0.563288:0.293662:0.563287:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.334916:0.578446:0.350249:0.578446:0.350249:0.564731:0.334916:0.564731:0.000000 x y:@0.358900:0.579001:0.380823:0.579001:0.380823:0.563566:0.358900:0.563566:0.000000:0.000000:0.000000 [:@0.389522:0.578711:0.404158:0.578711:0.404158:0.565301:0.389522:0.565301:0.000000 R:@0.408026:0.578141:0.421316:0.578141:0.421316:0.565244:0.408026:0.565244:0.000000 2:@0.421217:0.572937:0.426454:0.572937:0.426454:0.563777:0.421217:0.563777:0.000000 1:@0.577754:0.582173:0.582991:0.582173:0.582991:0.573013:0.577754:0.573013:0.000000 || || ( ) , y la distancia de a es:@0.293655:0.601717:0.665405:0.601717:0.665405:0.586004:0.293655:0.586004:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.313670:0.601162:0.329004:0.601162:0.329004:0.587447:0.313670:0.587447:0.000000 1:@0.341144:0.604889:0.346381:0.604889:0.346381:0.595729:0.341144:0.595729:0.000000 5:@0.357930:0.601162:0.373263:0.601162:0.373263:0.587447:0.357930:0.587447:0.000000 x:@0.393769:0.601717:0.401224:0.601717:0.401224:0.586282:0.393769:0.586282:0.000000 1:@0.405108:0.601162:0.420441:0.601162:0.420441:0.587447:0.405108:0.587447:0.000000 c:@0.424306:0.601717:0.431964:0.601717:0.431964:0.586282:0.424306:0.586282:0.000000 2:@0.436686:0.595653:0.441923:0.595653:0.441923:0.586493:0.436686:0.586493:0.000000 1:@0.445835:0.601162:0.461168:0.601162:0.461168:0.587447:0.445835:0.587447:0.000000 y:@0.465033:0.601717:0.472507:0.601717:0.472507:0.586282:0.465033:0.586282:0.000000 2:@0.472425:0.595653:0.477662:0.595653:0.477662:0.586493:0.472425:0.586493:0.000000 2:@0.640536:0.604889:0.645773:0.604889:0.645773:0.595729:0.640536:0.595729:0.000000 || || ( ) . Primeramente ( , , ) ≠ 0,:@0.293652:0.624433:0.694845:0.624434:0.694845:0.608722:0.293652:0.608720:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.313670:0.623880:0.329004:0.623880:0.329004:0.610164:0.313670:0.610164:0.000000 2:@0.341144:0.627607:0.346381:0.627607:0.346381:0.618446:0.341144:0.618446:0.000000 5:@0.357930:0.623880:0.373263:0.623880:0.373263:0.610164:0.357930:0.610164:0.000000 x:@0.393769:0.624434:0.401224:0.624434:0.401224:0.608999:0.393769:0.608999:0.000000 1:@0.405108:0.623880:0.420441:0.623880:0.420441:0.610164:0.405108:0.610164:0.000000 c:@0.424306:0.624434:0.431964:0.624434:0.431964:0.608999:0.424306:0.608999:0.000000 2:@0.436686:0.618370:0.441923:0.618370:0.441923:0.609210:0.436686:0.609210:0.000000 1:@0.445835:0.623880:0.461168:0.623880:0.461168:0.610164:0.445835:0.610164:0.000000 y:@0.465033:0.624434:0.472507:0.624434:0.472507:0.608999:0.465033:0.608999:0.000000 2:@0.472425:0.618370:0.477662:0.618370:0.477662:0.609210:0.472425:0.609210:0.000000 a b:@0.633677:0.624434:0.659190:0.624434:0.659190:0.608999:0.633677:0.608999:0.000000:0.000000:0.000000 pues ( , , ). En efecto, || || , || || , luego,:@0.293640:0.647151:0.751660:0.647152:0.751660:0.631439:0.293640:0.631438:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.344374:0.646862:0.359010:0.646862:0.359010:0.633452:0.344374:0.633452:0.000000 a b:@0.400508:0.647152:0.426020:0.647152:0.426020:0.631716:0.400508:0.631716:0.000000:0.000000:0.000000 2:@0.531510:0.646597:0.546844:0.646597:0.546844:0.632881:0.531510:0.632881:0.000000 1:@0.558984:0.650324:0.564221:0.650324:0.564221:0.641164:0.558984:0.641164:0.000000 5:@0.575770:0.646597:0.591103:0.646597:0.591103:0.632881:0.575770:0.632881:0.000000 c:@0.594968:0.647152:0.602626:0.647152:0.602626:0.631716:0.594968:0.631716:0.000000 2:@0.628625:0.646597:0.643959:0.646597:0.643959:0.632881:0.628625:0.632881:0.000000 2:@0.656099:0.650324:0.661336:0.650324:0.661336:0.641164:0.656099:0.641164:0.000000 5:@0.672885:0.646597:0.688218:0.646597:0.688218:0.632881:0.672885:0.632881:0.000000 c:@0.692083:0.647152:0.699741:0.647152:0.699741:0.631716:0.692083:0.631716:0.000000 || || || || 0 2 , lo que demuestra que :@0.293658:0.669868:0.680545:0.669869:0.680545:0.654156:0.293658:0.654155:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.312661:0.669314:0.327995:0.669314:0.327995:0.655599:0.312661:0.655599:0.000000 1:@0.340135:0.673042:0.345372:0.673042:0.345372:0.663881:0.340135:0.663881:0.000000 2:@0.356923:0.669314:0.372256:0.669314:0.372256:0.655599:0.356923:0.655599:0.000000 2:@0.395113:0.669314:0.410446:0.669314:0.410446:0.655599:0.395113:0.655599:0.000000 2:@0.422586:0.673042:0.427823:0.673042:0.427823:0.663881:0.422586:0.663881:0.000000 5 ,:@0.439374:0.669314:0.486754:0.669314:0.486754:0.655599:0.439374:0.655599:0.000000:0.000000:0.000000 a:@0.499510:0.669869:0.508769:0.669869:0.508769:0.654434:0.499510:0.654434:0.000000 [:@0.691672:0.669579:0.706308:0.669579:0.706308:0.656169:0.691672:0.656169:0.000000 ( , , ).:@0.706220:0.669869:0.781250:0.669869:0.781250:0.654156:0.706220:0.654156:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.747804:0.669869:0.773316:0.669869:0.773316:0.654434:0.747804:0.654434:0.000000:0.000000:0.000000 Por otro lado, de la propiedad de la norma siguiente::@0.293642:0.692585:0.673864:0.692585:0.673864:0.676873:0.293642:0.676873:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 | || || || || | || || :@0.293642:0.715301:0.475807:0.715304:0.475807:0.699591:0.293642:0.699589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.329086:0.714749:0.344419:0.714749:0.344419:0.701033:0.329086:0.701033:0.000000 #:@0.384937:0.714749:0.400270:0.714749:0.400270:0.701033:0.384937:0.701033:0.000000 2:@0.424139:0.714749:0.439472:0.714749:0.439472:0.701033:0.424139:0.701033:0.000000 ;:@0.475689:0.714749:0.487967:0.714749:0.487967:0.701033:0.475689:0.701033:0.000000 , :@0.496292:0.715304:0.503453:0.715304:0.503453:0.699591:0.496292:0.699591:0.000000:0.000000 :@0.512280:0.715845:0.516882:0.715845:0.516882:0.700673:0.512280:0.700673:0.000000 [:@0.516790:0.715014:0.531426:0.715014:0.531426:0.701604:0.516790:0.701604:0.000000 , así::@0.531338:0.715304:0.582815:0.715304:0.582815:0.699591:0.531338:0.699591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.535295:0.714444:0.548586:0.714444:0.548586:0.701547:0.535295:0.701547:0.000000 2:@0.548485:0.709240:0.553722:0.709240:0.553722:0.700079:0.548485:0.700079:0.000000 2 | || || || || | | || || || || | || || 2 ,:@0.293655:0.738020:0.808024:0.738021:0.808024:0.722309:0.293655:0.722307:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.302564:0.738020:0.311823:0.738020:0.311823:0.722585:0.302564:0.722585:0.000000 5:@0.315707:0.737465:0.331040:0.737465:0.331040:0.723750:0.315707:0.723750:0.000000 2:@0.362679:0.737466:0.378012:0.737466:0.378012:0.723751:0.362679:0.723751:0.000000 1:@0.390153:0.741194:0.395389:0.741194:0.395389:0.732033:0.390153:0.732033:0.000000 2:@0.406938:0.737466:0.422272:0.737466:0.422272:0.723751:0.406938:0.723751:0.000000 2:@0.446137:0.737466:0.461471:0.737466:0.461471:0.723751:0.446137:0.723751:0.000000 2:@0.473611:0.741194:0.478848:0.741194:0.478848:0.732033:0.473611:0.732033:0.000000 5:@0.498166:0.737466:0.513500:0.737466:0.513500:0.723751:0.498166:0.723751:0.000000 1:@0.541055:0.741194:0.546292:0.741194:0.546292:0.732033:0.541055:0.732033:0.000000 2:@0.550204:0.737466:0.565537:0.737466:0.565537:0.723751:0.550204:0.723751:0.000000 2:@0.589398:0.737466:0.604731:0.737466:0.604731:0.723751:0.589398:0.723751:0.000000 2:@0.628600:0.737466:0.643933:0.737466:0.643933:0.723751:0.628600:0.723751:0.000000 2:@0.656074:0.741194:0.661311:0.741194:0.661311:0.732033:0.656074:0.732033:0.000000 #:@0.680629:0.737466:0.695962:0.737466:0.695962:0.723751:0.680629:0.723751:0.000000 1:@0.715747:0.741194:0.720984:0.741194:0.720984:0.732033:0.715747:0.732033:0.000000 2:@0.724894:0.737466:0.740227:0.737466:0.740227:0.723751:0.724894:0.723751:0.000000 2:@0.752361:0.741194:0.757597:0.741194:0.757597:0.732033:0.752361:0.732033:0.000000 5:@0.769148:0.737466:0.784481:0.737466:0.784481:0.723751:0.769148:0.723751:0.000000 c:@0.797237:0.738021:0.804895:0.738021:0.804895:0.722586:0.797237:0.722586:0.000000 con lo que si ( , , ), resulta::@0.293652:0.760737:0.546863:0.760739:0.546863:0.745026:0.293652:0.745025:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.401977:0.760449:0.416613:0.760449:0.416613:0.747039:0.401977:0.747039:0.000000 a b:@0.458109:0.760739:0.483621:0.760739:0.483621:0.745303:0.458109:0.745303:0.000000:0.000000:0.000000 2 | || || || || | || ||.:@0.293640:0.783455:0.585949:0.783456:0.585949:0.767743:0.293640:0.767742:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.302549:0.783455:0.311808:0.783455:0.311808:0.768019:0.302549:0.768019:0.000000 5:@0.315692:0.782900:0.331025:0.782900:0.331025:0.769184:0.315692:0.769184:0.000000 2:@0.362679:0.782901:0.378012:0.782901:0.378012:0.769186:0.362679:0.769186:0.000000 1:@0.390153:0.786628:0.395389:0.786628:0.395389:0.777468:0.390153:0.777468:0.000000 2:@0.406938:0.782901:0.422272:0.782901:0.422272:0.769186:0.406938:0.769186:0.000000 2:@0.446137:0.782901:0.461471:0.782901:0.461471:0.769186:0.446137:0.769186:0.000000 2:@0.473611:0.786628:0.478848:0.786628:0.478848:0.777468:0.473611:0.777468:0.000000 #:@0.498166:0.782901:0.513500:0.782901:0.513500:0.769186:0.498166:0.769186:0.000000 1:@0.533284:0.786628:0.538521:0.786628:0.538521:0.777468:0.533284:0.777468:0.000000 2:@0.542431:0.782901:0.557764:0.782901:0.557764:0.769186:0.542431:0.769186:0.000000 2:@0.569898:0.786628:0.575135:0.786628:0.575135:0.777468:0.569898:0.777468:0.000000 En la Figura 2.35. se muestran los focos , y un punto:@0.293660:0.810818:0.695853:0.810819:0.695853:0.795106:0.293660:0.795105:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.585857:0.813992:0.591094:0.813992:0.591094:0.804831:0.585857:0.804831:0.000000 2:@0.606403:0.813992:0.611640:0.813992:0.611640:0.804831:0.606403:0.804831:0.000000 ( , ) que pertenece a la hipérbola ( , , ). :@0.302077:0.838182:0.691553:0.838182:0.691553:0.822470:0.302077:0.822470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.307867:0.837628:0.323200:0.837628:0.323200:0.823912:0.307867:0.823912:0.000000 x y:@0.331852:0.838182:0.353775:0.838182:0.353775:0.822747:0.331852:0.822747:0.000000:0.000000:0.000000 [:@0.362473:0.837892:0.377109:0.837892:0.377109:0.824482:0.362473:0.824482:0.000000 R:@0.380979:0.837323:0.394269:0.837323:0.394269:0.824425:0.380979:0.824425:0.000000 2:@0.394169:0.832118:0.399406:0.832118:0.399406:0.822958:0.394169:0.822958:0.000000 a b:@0.654076:0.838182:0.679588:0.838182:0.679588:0.822747:0.654076:0.822747:0.000000:0.000000:0.000000 Obtengamos la ecuación cartesiana de la hipérbola. De la definición del conjunto :@0.293643:0.865544:0.892792:0.865544:0.892792:0.849832:0.293643:0.849832:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( , :@0.911469:0.865544:0.930943:0.865544:0.930943:0.849832:0.911469:0.849832:0.000000:0.000000:0.000000:0.000000 a b:@0.293660:0.882186:0.319173:0.882186:0.319173:0.866751:0.293660:0.866751:0.000000:0.000000:0.000000 , ) se sigue que::@0.302845:0.882186:0.422134:0.882186:0.422134:0.866473:0.302845:0.866473:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( , ) ( , , ) | || || || || | 2:@0.302077:0.909550:0.661392:0.909550:0.661392:0.893837:0.302077:0.893837:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.305290:0.908995:0.320623:0.908995:0.320623:0.895279:0.305290:0.895279:0.000000 x y:@0.329275:0.909550:0.351198:0.909550:0.351198:0.894115:0.329275:0.894115:0.000000:0.000000:0.000000 [:@0.359896:0.909260:0.374532:0.909260:0.374532:0.895850:0.359896:0.895850:0.000000 a b:@0.416028:0.909550:0.441541:0.909550:0.441541:0.894115:0.416028:0.894115:0.000000:0.000000:0.000000 2:@0.497723:0.908995:0.513056:0.908995:0.513056:0.895279:0.497723:0.895279:0.000000 1:@0.525197:0.912722:0.530433:0.912722:0.530433:0.903562:0.525197:0.903562:0.000000 2:@0.541984:0.908995:0.557317:0.908995:0.557317:0.895279:0.541984:0.895279:0.000000 2:@0.581183:0.908995:0.596516:0.908995:0.596516:0.895279:0.581183:0.895279:0.000000 2:@0.608657:0.912722:0.613894:0.912722:0.613894:0.903562:0.608657:0.903562:0.000000 5:@0.633210:0.908995:0.648544:0.908995:0.648544:0.895279:0.633210:0.895279:0.000000 a:@0.661300:0.909550:0.670559:0.909550:0.670559:0.894115:0.661300:0.894115:0.000000 ( ) ( ) :@0.309417:0.936913:0.524864:0.936913:0.524864:0.921200:0.309417:0.921200:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 |:@0.313368:0.937606:0.317270:0.937606:0.317270:0.918751:0.313368:0.918751:0.000000 x:@0.333828:0.936913:0.341283:0.936913:0.341283:0.921478:0.333828:0.921478:0.000000 1:@0.345167:0.936358:0.360500:0.936358:0.360500:0.922643:0.345167:0.922643:0.000000 c:@0.364366:0.936913:0.372023:0.936913:0.372023:0.921478:0.364366:0.921478:0.000000 2:@0.376755:0.930849:0.381992:0.930849:0.381992:0.921689:0.376755:0.921689:0.000000 1:@0.385904:0.936358:0.401237:0.936358:0.401237:0.922643:0.385904:0.922643:0.000000 y:@0.405103:0.936913:0.412576:0.936913:0.412576:0.921478:0.405103:0.921478:0.000000 2:@0.412494:0.930849:0.417731:0.930849:0.417731:0.921689:0.412494:0.921689:0.000000 2:@0.421642:0.936358:0.436976:0.936358:0.436976:0.922643:0.421642:0.922643:0.000000 x:@0.453524:0.936913:0.460979:0.936913:0.460979:0.921478:0.453524:0.921478:0.000000 2:@0.464863:0.936358:0.480196:0.936358:0.480196:0.922643:0.464863:0.922643:0.000000 c:@0.484061:0.936913:0.491719:0.936913:0.491719:0.921478:0.484061:0.921478:0.000000 2:@0.496444:0.930849:0.501681:0.930849:0.501681:0.921689:0.496444:0.921689:0.000000 1:@0.505591:0.936358:0.520924:0.936358:0.520924:0.922643:0.505591:0.922643:0.000000 y:@0.524790:0.936913:0.532263:0.936913:0.532263:0.921478:0.524790:0.921478:0.000000 2 :@0.532183:0.930849:0.542571:0.930849:0.542571:0.921689:0.532183:0.921689:0.000000:0.000000:0.000000 |:@0.542514:0.937606:0.546417:0.937606:0.546417:0.918751:0.542514:0.918751:0.000000 2:@0.546336:0.936913:0.578476:0.936913:0.578476:0.921200:0.546336:0.921200:0.000000:0.000000:0.000000:0.000000 5:@0.550294:0.936358:0.565627:0.936358:0.565627:0.922643:0.550294:0.922643:0.000000 a.:@0.578384:0.936913:0.590900:0.936913:0.590900:0.921478:0.578384:0.921478:0.000000:0.000000 Tema 6. Ecuación cartesiana de la hipérbola:@0.073089:0.098522:0.725368:0.098522:0.725368:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ¿Qué importancia tienen los dos puntos fijos llamados focos para el cálculo de la :@0.310262:0.162925:0.914253:0.162925:0.914253:0.147212:0.310262:0.147212:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ecuación cartesiana de la hipérbola?:@0.310262:0.179567:0.573852:0.179567:0.573852:0.163854:0.310262:0.163854:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Reto matemático:@0.302768:0.139600:0.433046:0.139600:0.433046:0.122930:0.302768:0.122930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Aprende la definición :@0.082576:0.289873:0.227852:0.289873:0.227852:0.275589:0.082576:0.275589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de la exentricidad de la :@0.082576:0.305002:0.238756:0.305002:0.238756:0.290718:0.082576:0.290718:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 hipérbola::@0.082576:0.320131:0.149053:0.320131:0.149053:0.305847:0.082576:0.305847:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sean , , , tal que :@0.082576:0.335260:0.246066:0.335260:0.246066:0.320976:0.082576:0.320976:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b c:@0.118403:0.335260:0.153912:0.335260:0.153912:0.321228:0.118403:0.321228:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.157130:0.335134:0.171069:0.335134:0.171069:0.322362:0.157130:0.322362:0.000000 R:@0.174242:0.334478:0.186324:0.334478:0.186324:0.322753:0.174242:0.322753:0.000000 2:@0.186073:0.329747:0.190834:0.329747:0.190834:0.321420:0.186073:0.321420:0.000000 0 y , :@0.082576:0.350389:0.248268:0.350389:0.248268:0.336105:0.082576:0.336105:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , ,:@0.094256:0.349884:0.137429:0.349884:0.137429:0.337416:0.094256:0.337416:0.000000:0.000000:0.000000 a:@0.111709:0.350389:0.120127:0.350389:0.120127:0.336357:0.111709:0.336357:0.000000 c b:@0.140944:0.350389:0.170562:0.350389:0.170562:0.336357:0.140944:0.336357:0.000000:0.000000:0.000000 2:@0.170497:0.344876:0.175258:0.344876:0.175258:0.336548:0.170497:0.336548:0.000000 5:@0.178715:0.349884:0.192655:0.349884:0.192655:0.337416:0.178715:0.337416:0.000000 c:@0.196169:0.350389:0.203130:0.350389:0.203130:0.336357:0.196169:0.336357:0.000000 2:@0.203056:0.344876:0.207817:0.344876:0.207817:0.336548:0.203056:0.336548:0.000000 2:@0.211274:0.349884:0.225214:0.349884:0.225214:0.337416:0.211274:0.337416:0.000000 a:@0.228728:0.350389:0.237145:0.350389:0.237145:0.336357:0.228728:0.336357:0.000000 2:@0.237071:0.344876:0.241832:0.344876:0.241832:0.336548:0.237071:0.336548:0.000000 F:@0.082569:0.365518:0.089882:0.365518:0.089882:0.351486:0.082569:0.351486:0.000000 :@0.085129:0.363702:0.090702:0.363702:0.090702:0.349910:0.085129:0.349910:0.000000 1:@0.089292:0.368402:0.094053:0.368402:0.094053:0.360074:0.089292:0.360074:0.000000 (:@0.094011:0.365518:0.119496:0.365518:0.119496:0.351233:0.094011:0.351233:0.000000:0.000000:0.000000:0.000000 5 2:@0.097608:0.365013:0.133352:0.365013:0.133352:0.352545:0.097608:0.352545:0.000000:0.000000:0.000000 c:@0.132766:0.365518:0.139727:0.365518:0.139727:0.351486:0.132766:0.351486:0.000000 , 0), ( , 0),:@0.139661:0.365518:0.236039:0.365518:0.236039:0.351233:0.139661:0.351233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 F:@0.167723:0.365518:0.175036:0.365518:0.175036:0.351486:0.167723:0.351486:0.000000 :@0.170283:0.363702:0.175856:0.363702:0.175856:0.349910:0.170283:0.349910:0.000000 2:@0.174448:0.368402:0.179209:0.368402:0.179209:0.360074:0.174448:0.360074:0.000000 5:@0.182765:0.365013:0.196704:0.365013:0.196704:0.352545:0.182765:0.352545:0.000000 c:@0.204569:0.365518:0.211530:0.365518:0.211530:0.351486:0.204569:0.351486:0.000000 los focos de la hipérbola :@0.082579:0.380647:0.246156:0.380647:0.246156:0.366362:0.082579:0.366362:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (0, , ).:@0.099421:0.395776:0.147836:0.395781:0.147836:0.381496:0.099421:0.381491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.105599:0.393965:0.111172:0.393965:0.111172:0.380173:0.105599:0.380173:0.000000 a b:@0.117430:0.395781:0.140623:0.395781:0.140623:0.381749:0.117430:0.381749:0.000000:0.000000:0.000000 La excentricidad de la :@0.082557:0.410910:0.229401:0.410910:0.229401:0.396625:0.082557:0.396625:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 hipérbola se define como:@0.082557:0.426039:0.251696:0.426039:0.251696:0.411754:0.082557:0.411754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 e:@0.107490:0.446702:0.114569:0.446702:0.114569:0.432670:0.107490:0.432670:0.000000 :@0.114502:0.446702:0.169607:0.446696:0.169607:0.432412:0.114502:0.432418:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.118099:0.446198:0.132039:0.446198:0.132039:0.433729:0.118099:0.433729:0.000000 c:@0.138412:0.438641:0.145721:0.438641:0.145721:0.423908:0.138412:0.423908:0.000000 a:@0.137639:0.453599:0.146476:0.453599:0.146476:0.438866:0.137639:0.438866:0.000000 5:@0.152087:0.446192:0.166026:0.446192:0.166026:0.433723:0.152087:0.433723:0.000000 a:@0.172760:0.440460:0.184760:0.440460:0.184760:0.425727:0.172760:0.425727:0.000000:0.000000 2:@0.184759:0.434672:0.190014:0.434672:0.190014:0.425396:0.184759:0.425396:0.000000 :@0.190014:0.440460:0.212099:0.440460:0.212099:0.424549:0.190014:0.424549:0.000000:0.000000:0.000000 1:@0.193739:0.439931:0.208374:0.439931:0.208374:0.426839:0.193739:0.426839:0.000000 b:@0.212099:0.440460:0.220937:0.440460:0.220937:0.425727:0.212099:0.425727:0.000000 2:@0.220936:0.434672:0.226191:0.434672:0.226191:0.425396:0.220936:0.425396:0.000000 a:@0.195056:0.455424:0.203893:0.455424:0.203893:0.440691:0.195056:0.440691:0.000000 .:@0.227863:0.446696:0.230774:0.446696:0.230774:0.432412:0.227863:0.432412:0.000000 Como se tiene que:@0.082576:0.465399:0.250584:0.465399:0.250584:0.451115:0.082576:0.451115:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c:@0.126820:0.465399:0.133781:0.465399:0.133781:0.451367:0.126820:0.451367:0.000000 .:@0.137312:0.464895:0.151251:0.464895:0.151251:0.452426:0.137312:0.452426:0.000000 a,:@0.154766:0.465399:0.166145:0.465399:0.166145:0.451367:0.154766:0.451367:0.000000:0.000000 e:@0.082592:0.486063:0.089671:0.486063:0.089671:0.472030:0.082592:0.472030:0.000000 1.:@0.089604:0.486063:0.155613:0.486061:0.155613:0.471777:0.089604:0.471778:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.093202:0.485558:0.107141:0.485558:0.107141:0.473090:0.093202:0.473090:0.000000 c:@0.113474:0.478005:0.120783:0.478005:0.120783:0.463272:0.113474:0.463272:0.000000 a:@0.112701:0.492963:0.121538:0.492963:0.121538:0.478230:0.112701:0.478230:0.000000 .:@0.127149:0.485557:0.141088:0.485557:0.141088:0.473088:0.127149:0.473088:0.000000 Competencia :@0.078581:0.252516:0.184211:0.252516:0.184211:0.235846:0.078581:0.235846:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.078581:0.269158:0.172830:0.269158:0.172830:0.252488:0.078581:0.252488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Figura 2.35.:@0.038303:0.744834:0.098492:0.744834:0.098492:0.733407:0.038303:0.733407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.143907:0.679429:0.148807:0.679429:0.148807:0.670859:0.143907:0.670859:0.000000 y:@0.134685:0.617484:0.141680:0.617484:0.141680:0.603914:0.134685:0.603914:0.000000 x:@0.251561:0.685358:0.258381:0.685358:0.258381:0.671788:0.251561:0.671788:0.000000 b:@0.141986:0.658970:0.147036:0.658970:0.147036:0.650551:0.141986:0.650551:0.000000 c:@0.180521:0.670120:0.184698:0.670120:0.184698:0.661701:0.180521:0.661701:0.000000 –a:@0.119837:0.675899:0.130148:0.675899:0.130148:0.667480:0.119837:0.667480:0.000000:0.000000 –c:@0.105489:0.670120:0.114988:0.670120:0.114988:0.661701:0.105489:0.661701:0.000000:0.000000 –b:@0.136966:0.690491:0.147036:0.690491:0.147036:0.682072:0.136966:0.682072:0.000000:0.000000 F:@0.181973:0.681907:0.187458:0.681907:0.187458:0.671383:0.181973:0.671383:0.000000 :@0.183944:0.681018:0.188123:0.681018:0.188123:0.670673:0.183944:0.670673:0.000000 1:@0.186806:0.682808:0.190377:0.682808:0.190377:0.676563:0.186806:0.676563:0.000000 F:@0.104954:0.681907:0.110438:0.681907:0.110438:0.671383:0.104954:0.671383:0.000000 :@0.106924:0.681018:0.111103:0.681018:0.111103:0.670673:0.106924:0.670673:0.000000 2:@0.109785:0.682808:0.113356:0.682808:0.113356:0.676563:0.109785:0.676563:0.000000 x:@0.200511:0.654289:0.205594:0.654289:0.205594:0.643765:0.200511:0.643765:0.000000 :@0.201829:0.654658:0.206008:0.654658:0.206008:0.644313:0.201829:0.644313:0.000000 x:@0.192127:0.669021:0.197210:0.669021:0.197210:0.658497:0.192127:0.658497:0.000000 :@0.193445:0.669389:0.197624:0.669389:0.197624:0.659045:0.193445:0.659045:0.000000 :@0.197624:0.669021:0.213576:0.669021:0.213576:0.658307:0.197624:0.658307:0.000000:0.000000:0.000000 2:@0.200373:0.668642:0.210827:0.668642:0.210827:0.659291:0.200373:0.659291:0.000000 F:@0.213576:0.669021:0.219061:0.669021:0.219061:0.658497:0.213576:0.658497:0.000000 :@0.215546:0.668132:0.219726:0.668132:0.219726:0.657787:0.215546:0.657787:0.000000 1:@0.218413:0.669923:0.221984:0.669923:0.221984:0.663678:0.218413:0.663678:0.000000 x:@0.154041:0.647429:0.159124:0.647429:0.159124:0.636905:0.154041:0.636905:0.000000 :@0.155359:0.647798:0.159538:0.647798:0.159538:0.637453:0.155359:0.637453:0.000000 :@0.159538:0.647429:0.175301:0.647429:0.175301:0.636716:0.159538:0.636716:0.000000:0.000000:0.000000 2:@0.162098:0.647051:0.172553:0.647051:0.172553:0.637699:0.162098:0.637699:0.000000 F:@0.175113:0.647429:0.180598:0.647429:0.180598:0.636905:0.175113:0.636905:0.000000 :@0.177084:0.646540:0.181263:0.646540:0.181263:0.636196:0.177084:0.636196:0.000000 2:@0.179942:0.648332:0.183512:0.648332:0.183512:0.642086:0.179942:0.642086:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000