123:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000
Pensamiento espacial, métrico y variacional:@0.541231:0.043660:0.930030:0.043660:0.930030:0.024915:0.541231:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Otra forma de presentar la :@0.744288:0.391725:0.921073:0.391725:0.921073:0.377441:0.744288:0.377441:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecuación canónica de la :@0.744288:0.406854:0.907192:0.406854:0.907192:0.392570:0.744288:0.392570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
elipse es::@0.744288:0.421983:0.803375:0.421983:0.803375:0.407698:0.744288:0.407698:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Forma ordinaria o :@0.744288:0.437112:0.864477:0.437112:0.864477:0.422827:0.744288:0.422827:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
canónica de la elipse  :@0.744288:0.452241:0.888568:0.452241:0.888568:0.437956:0.744288:0.437956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.744288:0.467370:0.753291:0.467370:0.753291:0.453337:0.744288:0.453337:0.000000
(0, 0):@0.753224:0.467370:0.784667:0.467370:0.784667:0.453085:0.753224:0.453085:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Eje mayor eje  : :@0.744288:0.482498:0.849143:0.482498:0.849143:0.468214:0.744288:0.468214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.835856:0.482498:0.842633:0.482498:0.842633:0.468466:0.835856:0.468466:0.000000
a:@0.745168:0.513775:0.754427:0.513775:0.754427:0.498340:0.745168:0.498340:0.000000
:@0.754427:0.514090:0.760170:0.514090:0.760170:0.496949:0.754427:0.496949:0.000000
x  :@0.747802:0.499559:0.765292:0.499559:0.765292:0.482720:0.747802:0.482720:0.000000:0.000000:0.000000
:@0.755935:0.499559:0.761678:0.499559:0.761678:0.482418:0.755935:0.482418:0.000000
   :@0.763306:0.504699:0.784418:0.504699:0.784418:0.490415:0.763306:0.490415:0.000000:0.000000:0.000000
1:@0.766897:0.504195:0.780837:0.504195:0.780837:0.491726:0.766897:0.491726:0.000000
b:@0.784925:0.512532:0.794183:0.512532:0.794183:0.497097:0.784925:0.497097:0.000000
:@0.794182:0.512847:0.799925:0.512847:0.799925:0.495706:0.794182:0.495706:0.000000
y  :@0.788934:0.496180:0.806444:0.496180:0.806444:0.479342:0.788934:0.479342:0.000000:0.000000:0.000000
:@0.797087:0.496180:0.802830:0.496180:0.802830:0.479039:0.797087:0.479039:0.000000
   1:@0.803364:0.504699:0.832574:0.504699:0.832574:0.490415:0.803364:0.490415:0.000000:0.000000:0.000000:0.000000
5:@0.806955:0.504195:0.820894:0.504195:0.820894:0.491726:0.806955:0.491726:0.000000
 :@0.744286:0.519828:0.747951:0.519828:0.747951:0.505544:0.744286:0.505544:0.000000
Eje mayor eje  ::@0.744286:0.534957:0.845493:0.534957:0.845493:0.520673:0.744286:0.520673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.835854:0.534957:0.842648:0.534957:0.842648:0.520925:0.835854:0.520925:0.000000
a:@0.744867:0.572623:0.754126:0.572623:0.754126:0.557188:0.744867:0.557188:0.000000
:@0.754126:0.572938:0.759869:0.572938:0.759869:0.555797:0.754126:0.555797:0.000000
y  :@0.748877:0.556271:0.766387:0.556271:0.766387:0.539432:0.748877:0.539432:0.000000:0.000000:0.000000
:@0.757029:0.556271:0.762772:0.556271:0.762772:0.539130:0.757029:0.539130:0.000000
 :@0.763306:0.565700:0.766971:0.565700:0.766971:0.551416:0.763306:0.551416:0.000000
1 :@0.766897:0.565196:0.784936:0.565196:0.784936:0.552727:0.766897:0.552727:0.000000:0.000000
b:@0.785433:0.572137:0.794692:0.572137:0.794692:0.556702:0.785433:0.556702:0.000000
:@0.794691:0.572453:0.800434:0.572453:0.800434:0.555312:0.794691:0.555312:0.000000
x  :@0.789443:0.555786:0.806933:0.555786:0.806933:0.538947:0.789443:0.538947:0.000000:0.000000:0.000000
:@0.797575:0.555786:0.803318:0.555786:0.803318:0.538644:0.797575:0.538644:0.000000
 5:@0.803861:0.565196:0.821900:0.565196:0.821900:0.552727:0.803861:0.552727:0.000000:0.000000
 1:@0.821816:0.565700:0.833580:0.565700:0.833580:0.551416:0.821816:0.551416:0.000000:0.000000
Ecuación canónica de la :@0.744288:0.587977:0.906801:0.587977:0.906801:0.573693:0.744288:0.573693:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
elipse con  ( ,  ):@0.744288:0.603106:0.854447:0.603106:0.854447:0.588822:0.744288:0.588822:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C h k:@0.814905:0.603106:0.850080:0.603106:0.850080:0.589074:0.814905:0.589074:0.000000:0.000000:0.000000:0.000000:0.000000
Eje mayor paralelo al eje  ::@0.744271:0.618235:0.916530:0.618235:0.916530:0.603951:0.744271:0.603951:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.906908:0.618235:0.913685:0.618235:0.913685:0.604203:0.906908:0.604203:0.000000
a:@0.761132:0.651340:0.770391:0.651340:0.770391:0.635905:0.761132:0.635905:0.000000
:@0.770390:0.651655:0.776133:0.651655:0.776133:0.634514:0.770390:0.634514:0.000000
(:@0.744688:0.634988:0.750009:0.634988:0.750009:0.617847:0.744688:0.617847:0.000000
x h   y k  :@0.750009:0.634988:0.867742:0.634396:0.867742:0.617557:0.750009:0.618150:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.758142:0.634383:0.774869:0.634383:0.774869:0.619420:0.758142:0.619420:0.000000
)² (:@0.785229:0.634988:0.819930:0.634396:0.819930:0.617254:0.785229:0.617847:0.000000:0.000000:0.000000:0.000000
 :@0.796762:0.644990:0.800427:0.644990:0.800427:0.630705:0.796762:0.630705:0.000000
1:@0.800355:0.644485:0.814294:0.644485:0.814294:0.632017:0.800355:0.632017:0.000000
b:@0.831053:0.650747:0.840312:0.650747:0.840312:0.635312:0.831053:0.635312:0.000000
:@0.840312:0.651063:0.846055:0.651063:0.846055:0.633922:0.840312:0.633922:0.000000
2:@0.828081:0.633790:0.844808:0.633790:0.844808:0.618828:0.828081:0.618828:0.000000
)²:@0.853063:0.634396:0.864128:0.634396:0.864128:0.617254:0.853063:0.617254:0.000000:0.000000
 5:@0.866673:0.644485:0.884712:0.644485:0.884712:0.632017:0.866673:0.632017:0.000000:0.000000
 1:@0.884628:0.644990:0.896392:0.644990:0.896392:0.630705:0.884628:0.630705:0.000000:0.000000
Eje mayor paralelo al eje  ::@0.744281:0.660119:0.916557:0.660119:0.916557:0.645834:0.744281:0.645834:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.906918:0.660119:0.913712:0.660119:0.913712:0.646086:0.906918:0.646086:0.000000
a:@0.761132:0.692632:0.770391:0.692632:0.770391:0.677197:0.761132:0.677197:0.000000
:@0.770390:0.692947:0.776133:0.692947:0.776133:0.675806:0.770390:0.675806:0.000000
(:@0.744686:0.676280:0.750008:0.676280:0.750008:0.659139:0.744686:0.659139:0.000000
y k  :@0.750008:0.676280:0.797820:0.676280:0.797820:0.659442:0.750008:0.659442:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.758160:0.675675:0.774888:0.675675:0.774888:0.660712:0.758160:0.660712:0.000000
)²:@0.783141:0.676280:0.794205:0.676280:0.794205:0.659139:0.783141:0.659139:0.000000:0.000000
 :@0.796762:0.686843:0.800427:0.686843:0.800427:0.672558:0.796762:0.672558:0.000000
1 :@0.800355:0.686338:0.818394:0.686338:0.818394:0.673869:0.800355:0.673869:0.000000:0.000000
b:@0.834853:0.695511:0.844112:0.695511:0.844112:0.680076:0.834853:0.680076:0.000000
:@0.844112:0.695827:0.849855:0.695827:0.849855:0.678686:0.844112:0.678686:0.000000
(:@0.818709:0.679161:0.824030:0.679161:0.824030:0.662020:0.818709:0.662020:0.000000
x h  :@0.824030:0.679161:0.873929:0.679161:0.873929:0.662322:0.824030:0.662322:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.832163:0.678556:0.848890:0.678556:0.848890:0.663593:0.832163:0.663593:0.000000
)²:@0.859250:0.679161:0.870314:0.679161:0.870314:0.662020:0.859250:0.662020:0.000000:0.000000
Competencia :@0.740294:0.354369:0.848854:0.354369:0.848854:0.337422:0.740294:0.337422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.740294:0.371011:0.837769:0.371011:0.837769:0.354064:0.740294:0.354064:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En este caso, la pendiente de dicha recta   sí está definida, por lo que se puede obtener :@0.073089:0.136836:0.710634:0.136836:0.710634:0.121124:0.073089:0.121124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.371782:0.136836:0.379403:0.136836:0.379403:0.121401:0.371782:0.121401:0.000000
su ecuación cartesiana.:@0.073088:0.153478:0.240616:0.153478:0.240616:0.137765:0.073088:0.137765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Supongamos que la ecuación cartesiana de la recta tangente   a la elipse  ( ,  ,  ) en el :@0.073088:0.182629:0.710382:0.182628:0.710382:0.166915:0.073088:0.166916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.521930:0.182629:0.529551:0.182629:0.529551:0.167194:0.521930:0.167194:0.000000
E:@0.608628:0.182629:0.616746:0.182629:0.616746:0.167194:0.608628:0.167194:0.000000
a b:@0.636182:0.182628:0.661897:0.182628:0.661897:0.167192:0.636182:0.167192:0.000000:0.000000:0.000000
punto     ( ,  ) está definida como::@0.073068:0.199270:0.340639:0.199270:0.340639:0.183557:0.073068:0.183557:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.133772:0.198715:0.149105:0.198715:0.149105:0.184999:0.133772:0.184999:0.000000
x y:@0.157757:0.199270:0.184552:0.199270:0.184552:0.183834:0.157757:0.183834:0.000000:0.000000:0.000000
0:@0.165057:0.202442:0.170294:0.202442:0.170294:0.193281:0.165057:0.193281:0.000000
0:@0.184396:0.202442:0.189633:0.202442:0.189633:0.193281:0.184396:0.193281:0.000000
( ,  )     tal que          (     ),:@0.256205:0.228421:0.523239:0.228419:0.523239:0.212707:0.256205:0.212708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.261009:0.228421:0.282932:0.228421:0.282932:0.212985:0.261009:0.212985:0.000000:0.000000:0.000000
[:@0.291610:0.228129:0.306247:0.228129:0.306247:0.214719:0.291610:0.214719:0.000000
R:@0.310116:0.227559:0.323406:0.227559:0.323406:0.214662:0.310116:0.214662:0.000000
2:@0.323308:0.222355:0.328544:0.222355:0.328544:0.213195:0.323308:0.213195:0.000000
y:@0.386498:0.228419:0.393971:0.228419:0.393971:0.212984:0.386498:0.212984:0.000000
2:@0.397855:0.227865:0.413188:0.227865:0.413188:0.214149:0.397855:0.214149:0.000000
y:@0.417054:0.228419:0.424527:0.228419:0.424527:0.212984:0.417054:0.212984:0.000000
0:@0.424445:0.231593:0.429682:0.231593:0.429682:0.222432:0.424445:0.222432:0.000000
5:@0.433592:0.227865:0.448925:0.227865:0.448925:0.214149:0.433592:0.214149:0.000000
m x:@0.452791:0.228419:0.479592:0.228419:0.479592:0.212984:0.452791:0.212984:0.000000:0.000000:0.000000
2:@0.483476:0.227865:0.498809:0.227865:0.498809:0.214149:0.483476:0.214149:0.000000
x:@0.502674:0.228419:0.510129:0.228419:0.510129:0.212984:0.502674:0.212984:0.000000
0:@0.510042:0.231593:0.515279:0.231593:0.515279:0.222432:0.510042:0.222432:0.000000
donde       es la pendiente de dicha recta   y de la que por el momento no se conoce. :@0.073089:0.257570:0.710478:0.257570:0.710478:0.241858:0.073089:0.241858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.124427:0.257570:0.139043:0.257570:0.139043:0.242135:0.124427:0.242135:0.000000
[:@0.142490:0.257280:0.157126:0.257280:0.157126:0.243870:0.142490:0.243870:0.000000
R:@0.160539:0.256710:0.173829:0.256710:0.173829:0.243813:0.160539:0.243813:0.000000
L:@0.394513:0.257570:0.402134:0.257570:0.402134:0.242135:0.394513:0.242135:0.000000
Cuando      , la ecuación precedente genera   haz de rectas que pasan por ( ,  ). En :@0.073068:0.274212:0.710390:0.274212:0.710390:0.258499:0.073068:0.258499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.134327:0.274212:0.148942:0.274212:0.148942:0.258777:0.134327:0.258777:0.000000
[:@0.152928:0.273922:0.167565:0.273922:0.167565:0.260512:0.152928:0.260512:0.000000
R:@0.171511:0.273352:0.184801:0.273352:0.184801:0.260455:0.171511:0.260455:0.000000
n:@0.419310:0.274212:0.428808:0.274212:0.428808:0.258777:0.419310:0.258777:0.000000
x y:@0.644154:0.274212:0.671235:0.274212:0.671235:0.258777:0.644154:0.258777:0.000000:0.000000:0.000000
0:@0.651465:0.277384:0.656702:0.277384:0.656702:0.268224:0.651465:0.268224:0.000000
0:@0.671072:0.277384:0.676309:0.277384:0.676309:0.268224:0.671072:0.268224:0.000000
la Figura 2.33. se muestran algunas rectas de este haz (cuatro rectas  ,  ,  ,   y la recta :@0.073094:0.290854:0.710403:0.290854:0.710403:0.275141:0.073094:0.275141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L L L L:@0.564660:0.290854:0.632360:0.290854:0.632360:0.275419:0.564660:0.275419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.572142:0.294026:0.577379:0.294026:0.577379:0.284866:0.572142:0.284866:0.000000
2:@0.592171:0.294026:0.597407:0.294026:0.597407:0.284866:0.592171:0.284866:0.000000
3:@0.612199:0.294026:0.617436:0.294026:0.617436:0.284866:0.612199:0.284866:0.000000
4:@0.632228:0.294026:0.637465:0.294026:0.637465:0.284866:0.632228:0.284866:0.000000
tangente  ).:@0.073094:0.307496:0.158173:0.307496:0.158173:0.291783:0.073094:0.291783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.142803:0.307496:0.150423:0.307496:0.150423:0.292060:0.142803:0.292060:0.000000
La ecuación cartesiana de la elipse  ( ,  ,  ) está definida como: :@0.073094:0.336647:0.533967:0.336645:0.533967:0.320933:0.073094:0.320934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E:@0.326065:0.336647:0.334183:0.336647:0.334183:0.321211:0.326065:0.321211:0.000000
a b:@0.353392:0.336645:0.378904:0.336645:0.378904:0.321210:0.353392:0.321210:0.000000:0.000000:0.000000
( ,  )     tal que :@0.263785:0.369901:0.394236:0.369900:0.394236:0.354187:0.263785:0.354189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.268589:0.369901:0.290512:0.369901:0.290512:0.354466:0.268589:0.354466:0.000000:0.000000:0.000000
[:@0.299219:0.369610:0.313855:0.369610:0.313855:0.356200:0.299219:0.356200:0.000000
R:@0.317725:0.369040:0.331015:0.369040:0.331015:0.356143:0.317725:0.356143:0.000000
2:@0.330916:0.363836:0.336153:0.363836:0.336153:0.354676:0.330916:0.354676:0.000000
a:@0.402101:0.375783:0.411359:0.375783:0.411359:0.360347:0.402101:0.360347:0.000000
( ) ( ):@0.393255:0.377699:0.475007:0.378400:0.475007:0.345484:0.393255:0.344783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.404316:0.363218:0.416063:0.363218:0.416063:0.346380:0.404316:0.346380:0.000000:0.000000
:@0.419839:0.363309:0.425582:0.363309:0.425582:0.346168:0.419839:0.346168:0.000000
   :@0.425677:0.369900:0.448900:0.369900:0.448900:0.354187:0.425677:0.354187:0.000000:0.000000:0.000000
1:@0.429628:0.369345:0.444961:0.369345:0.444961:0.355630:0.429628:0.355630:0.000000
b:@0.457424:0.378177:0.466683:0.378177:0.466683:0.362742:0.457424:0.362742:0.000000
y:@0.459280:0.362071:0.467433:0.362071:0.467433:0.345232:0.459280:0.345232:0.000000
:@0.474622:0.364007:0.480365:0.364007:0.480365:0.346866:0.474622:0.346866:0.000000
   1.:@0.480377:0.369900:0.515638:0.369900:0.515638:0.354187:0.480377:0.354187:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.484327:0.369345:0.499661:0.369345:0.499661:0.355630:0.484327:0.355630:0.000000
En el punto de tangencia,     ( ,  )    ( ,  ,  ); luego,:@0.073091:0.399051:0.467881:0.399050:0.467881:0.383337:0.073091:0.383338:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.274831:0.398495:0.290164:0.398495:0.290164:0.384779:0.274831:0.384779:0.000000
x y:@0.298816:0.399050:0.325940:0.399050:0.325940:0.383614:0.298816:0.383614:0.000000:0.000000:0.000000
0:@0.306209:0.402222:0.311446:0.402222:0.311446:0.393062:0.306209:0.393062:0.000000
0:@0.325878:0.402222:0.331115:0.402222:0.331115:0.393062:0.325878:0.393062:0.000000
[:@0.339815:0.398760:0.354452:0.398760:0.354452:0.385350:0.339815:0.385350:0.000000
E:@0.358321:0.399050:0.366439:0.399050:0.366439:0.383614:0.358321:0.383614:0.000000
a b:@0.385645:0.399050:0.411157:0.399050:0.411157:0.383614:0.385645:0.383614:0.000000:0.000000:0.000000
a:@0.336942:0.438187:0.346201:0.438187:0.346201:0.422752:0.336942:0.422752:0.000000
( ) ( ):@0.328097:0.440103:0.409786:0.442376:0.409786:0.409460:0.328097:0.407187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x  :@0.335148:0.425577:0.353121:0.425577:0.353121:0.408739:0.335148:0.408739:0.000000:0.000000:0.000000
₀ :@0.343281:0.425577:0.360410:0.425713:0.360410:0.408572:0.343281:0.408436:0.000000:0.000000:0.000000
   :@0.360520:0.434472:0.383744:0.434472:0.383744:0.418759:0.360520:0.418759:0.000000:0.000000:0.000000
1:@0.364471:0.433917:0.379804:0.433917:0.379804:0.420201:0.364471:0.420201:0.000000
b:@0.392084:0.442534:0.401343:0.442534:0.401343:0.427099:0.392084:0.427099:0.000000
y  :@0.390169:0.426408:0.408162:0.426408:0.408162:0.409569:0.390169:0.409569:0.000000:0.000000:0.000000
₀ :@0.398322:0.426408:0.415150:0.427981:0.415150:0.410840:0.398322:0.409267:0.000000:0.000000:0.000000
   1.:@0.415242:0.434472:0.450503:0.434472:0.450503:0.418759:0.415242:0.418759:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.419193:0.433917:0.434526:0.433917:0.434526:0.420201:0.419193:0.420201:0.000000
Se prueba que la pendiente     :@0.073081:0.470473:0.316241:0.470473:0.316241:0.454761:0.073081:0.454761:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.278469:0.470473:0.293084:0.470473:0.293084:0.455038:0.278469:0.455038:0.000000
5:@0.296968:0.469919:0.312302:0.469919:0.312302:0.456203:0.296968:0.456203:0.000000
a:@0.327091:0.476679:0.336350:0.476679:0.336350:0.461244:0.327091:0.461244:0.000000
 ₀:@0.336348:0.476994:0.356469:0.476994:0.356469:0.459066:0.336348:0.459066:0.000000:0.000000:0.000000
y:@0.342091:0.476994:0.350244:0.476994:0.350244:0.460156:0.342091:0.460156:0.000000
2:@0.314582:0.460488:0.331310:0.460488:0.331310:0.445526:0.314582:0.445526:0.000000
b  x  :@0.331310:0.461094:0.367274:0.460504:0.367274:0.443665:0.331310:0.444255:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
₀:@0.357435:0.460504:0.363660:0.460504:0.363660:0.442576:0.357435:0.442576:0.000000
:@0.342314:0.460594:0.348057:0.460594:0.348057:0.442666:0.342314:0.442666:0.000000
 y la ecuación de la recta es::@0.365592:0.470480:0.565814:0.470480:0.565814:0.454767:0.365592:0.454767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  )     tal que          :@0.258293:0.505013:0.458919:0.505013:0.458919:0.489300:0.258293:0.489300:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.263097:0.505013:0.285020:0.505013:0.285020:0.489578:0.263097:0.489578:0.000000:0.000000:0.000000
[:@0.293707:0.504723:0.308343:0.504723:0.308343:0.491313:0.293707:0.491313:0.000000
R:@0.312213:0.504153:0.325503:0.504153:0.325503:0.491256:0.312213:0.491256:0.000000
2:@0.325403:0.498949:0.330639:0.498949:0.330639:0.489788:0.325403:0.489788:0.000000
y:@0.388595:0.505013:0.396068:0.505013:0.396068:0.489578:0.388595:0.489578:0.000000
2:@0.399952:0.504458:0.415285:0.504458:0.415285:0.490742:0.399952:0.490742:0.000000
y:@0.419151:0.505013:0.426624:0.505013:0.426624:0.489578:0.419151:0.489578:0.000000
0:@0.426540:0.508185:0.431777:0.508185:0.431777:0.499025:0.426540:0.499025:0.000000
5:@0.435689:0.504458:0.451022:0.504458:0.451022:0.490742:0.435689:0.490742:0.000000
a:@0.470095:0.510253:0.479354:0.510253:0.479354:0.494817:0.470095:0.494817:0.000000
( ):@0.458137:0.511177:0.492596:0.511177:0.492596:0.478260:0.458137:0.478260:0.000000:0.000000:0.000000
2:@0.460400:0.496498:0.477127:0.496498:0.477127:0.481535:0.460400:0.481535:0.000000
b  x  :@0.477127:0.497103:0.520207:0.496742:0.520207:0.479904:0.477127:0.480264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.503192:0.509575:0.510665:0.509575:0.510665:0.494140:0.503192:0.494140:0.000000
₀ :@0.510665:0.509891:0.521288:0.509891:0.521288:0.492750:0.510665:0.492750:0.000000:0.000000
₀:@0.510367:0.496742:0.516592:0.496742:0.516592:0.479601:0.510367:0.479601:0.000000
:@0.492194:0.498316:0.497937:0.498316:0.497937:0.481175:0.492194:0.481175:0.000000
.:@0.517934:0.505013:0.521137:0.505013:0.521137:0.489300:0.517934:0.489300:0.000000
Ejercicio resuelto:@0.073089:0.534163:0.201671:0.534163:0.201671:0.517493:0.073089:0.517493:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Considérese la elipse  ( , 4, 1) y     :@0.073089:0.566739:0.332099:0.566740:0.332099:0.551028:0.073089:0.551026:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E:@0.227931:0.566739:0.236048:0.566739:0.236048:0.551304:0.227931:0.551304:0.000000
5:@0.312827:0.566185:0.328160:0.566185:0.328160:0.552470:0.312827:0.552470:0.000000
2:@0.332615:0.568348:0.349342:0.568348:0.349342:0.553385:0.332615:0.553385:0.000000
2, :@0.349342:0.568953:0.367033:0.568953:0.367033:0.551025:0.349342:0.551025:0.000000:0.000000:0.000000
3:@0.375807:0.562726:0.385606:0.562726:0.385606:0.544798:0.375807:0.544798:0.000000
(:@0.331050:0.575884:0.335928:0.575884:0.335928:0.541457:0.331050:0.541457:0.000000
):@0.391187:0.575449:0.396065:0.575449:0.396065:0.541021:0.391187:0.541021:0.000000
2:@0.371809:0.576527:0.381608:0.576527:0.381608:0.558600:0.371809:0.558600:0.000000
.:@0.394626:0.566740:0.397828:0.566740:0.397828:0.551028:0.394626:0.551028:0.000000
Determinamos la ecuación cartesiana de la recta tangente   en:@0.073089:0.595890:0.529405:0.595890:0.529405:0.580177:0.073089:0.580177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.499180:0.595890:0.506801:0.595890:0.506801:0.580455:0.499180:0.580455:0.000000
el punto  ( , 4, 1)     :@0.073089:0.629312:0.225826:0.629308:0.225826:0.613596:0.073089:0.613600:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E:@0.138435:0.629312:0.146552:0.629312:0.146552:0.613877:0.138435:0.613877:0.000000
5:@0.203332:0.628754:0.218666:0.628754:0.218666:0.615038:0.203332:0.615038:0.000000
2:@0.226335:0.630075:0.243062:0.630075:0.243062:0.615112:0.226335:0.615112:0.000000
2, :@0.243062:0.630680:0.260753:0.630680:0.260753:0.612752:0.243062:0.612752:0.000000:0.000000:0.000000
3:@0.269527:0.624453:0.279326:0.624453:0.279326:0.606526:0.269527:0.606526:0.000000
(:@0.224770:0.637613:0.229648:0.637613:0.229648:0.603186:0.224770:0.603186:0.000000
):@0.284907:0.637177:0.289785:0.637177:0.289785:0.602750:0.284907:0.602750:0.000000
2:@0.265529:0.638256:0.275328:0.638256:0.275328:0.620328:0.265529:0.620328:0.000000
. Primero, verificamos que:@0.288345:0.629308:0.474089:0.629308:0.474089:0.613596:0.288345:0.613596:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
    ( , 4, 1). En efecto, la ecuación cartesiana de la elipse es: :@0.081103:0.658459:0.514167:0.658459:0.514167:0.642747:0.081103:0.642747:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.085054:0.658169:0.099690:0.658169:0.099690:0.644759:0.085054:0.644759:0.000000
E:@0.103560:0.658459:0.111677:0.658459:0.111677:0.643024:0.103560:0.643024:0.000000
( ,  )    , tal que :@0.073089:0.692476:0.206647:0.692476:0.206647:0.676763:0.073089:0.676763:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.077893:0.692476:0.099816:0.692476:0.099816:0.677040:0.077893:0.677040:0.000000:0.000000:0.000000
[:@0.108502:0.692186:0.123138:0.692186:0.123138:0.678776:0.108502:0.678776:0.000000
R:@0.127008:0.691616:0.140298:0.691616:0.140298:0.678718:0.127008:0.678718:0.000000
2:@0.140199:0.686412:0.145436:0.686412:0.145436:0.677251:0.140199:0.677251:0.000000
a:@0.214506:0.697595:0.223764:0.697595:0.223764:0.682160:0.214506:0.682160:0.000000
( ) ( ):@0.205660:0.699513:0.287410:0.699759:0.287410:0.666842:0.205660:0.666597:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.216721:0.685032:0.228468:0.685032:0.228468:0.668194:0.216721:0.668194:0.000000:0.000000
:@0.232243:0.685123:0.237987:0.685123:0.237987:0.667982:0.232243:0.667982:0.000000
   :@0.238082:0.692476:0.261305:0.692476:0.261305:0.676763:0.238082:0.676763:0.000000:0.000000:0.000000
1:@0.242033:0.691921:0.257366:0.691921:0.257366:0.678205:0.242033:0.678205:0.000000
b:@0.269829:0.699536:0.279088:0.699536:0.279088:0.684100:0.269829:0.684100:0.000000
y:@0.271685:0.683430:0.279838:0.683430:0.279838:0.666591:0.271685:0.666591:0.000000
:@0.287027:0.685366:0.292770:0.685366:0.292770:0.668225:0.287027:0.668225:0.000000
   1.:@0.292782:0.692476:0.328042:0.692476:0.328042:0.676763:0.292782:0.676763:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.296731:0.691921:0.312064:0.691921:0.312064:0.678205:0.296731:0.678205:0.000000
Luego, para   :@0.073083:0.728422:0.187373:0.728422:0.187373:0.712709:0.073083:0.712709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.175445:0.728422:0.182900:0.728422:0.182900:0.712987:0.175445:0.712987:0.000000
5 2:@0.191018:0.727867:0.229968:0.727867:0.229968:0.714152:0.191018:0.714152:0.000000:0.000000:0.000000
 :@0.206959:0.728422:0.210990:0.728422:0.210990:0.712709:0.206959:0.712709:0.000000
2,   :@0.230575:0.728422:0.263469:0.728422:0.263469:0.712709:0.230575:0.712709:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.251523:0.728422:0.258996:0.728422:0.258996:0.712987:0.251523:0.712987:0.000000
5 2:@0.267114:0.727867:0.304775:0.727867:0.304775:0.714152:0.267114:0.714152:0.000000:0.000000:0.000000
   :@0.283054:0.728422:0.309413:0.728422:0.309413:0.712709:0.283054:0.712709:0.000000:0.000000:0.000000
3:@0.324696:0.721039:0.334496:0.721039:0.334496:0.703898:0.324696:0.703898:0.000000
2:@0.320697:0.734842:0.330496:0.734842:0.330496:0.717701:0.320697:0.717701:0.000000
 se tiene :@0.336996:0.728421:0.413165:0.728421:0.413165:0.712708:0.336996:0.712708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.441293:0.721014:0.451092:0.721014:0.451092:0.703873:0.441293:0.703873:0.000000
4:@0.441173:0.734811:0.450972:0.734811:0.450972:0.717670:0.441173:0.717670:0.000000
( ) (:@0.416990:0.734039:0.504395:0.736052:0.504395:0.703136:0.416990:0.701122:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.415417:0.727607:0.419815:0.727607:0.419815:0.710466:0.415417:0.710466:0.000000
2:@0.419815:0.727002:0.436542:0.727002:0.436542:0.712040:0.419815:0.712040:0.000000
₂:@0.461508:0.713888:0.467251:0.713888:0.467251:0.696747:0.461508:0.696747:0.000000
 :@0.468710:0.728421:0.472741:0.728421:0.472741:0.712708:0.468710:0.712708:0.000000
1:@0.476386:0.727866:0.491719:0.727866:0.491719:0.714150:0.476386:0.714150:0.000000
 :@0.492326:0.728421:0.496357:0.728421:0.496357:0.712708:0.492326:0.712708:0.000000
₂ :@0.549995:0.716180:0.560135:0.716180:0.560135:0.699039:0.549995:0.699039:0.000000:0.000000
3:@0.528649:0.722897:0.538448:0.722897:0.538448:0.705756:0.528649:0.705756:0.000000
):@0.544026:0.735616:0.548903:0.735616:0.548903:0.702700:0.544026:0.702700:0.000000
2:@0.524648:0.736695:0.534447:0.736695:0.534447:0.719554:0.524648:0.719554:0.000000
2:@0.500497:0.729344:0.517225:0.729344:0.517225:0.714381:0.500497:0.714381:0.000000
 :@0.556509:0.728421:0.560540:0.728421:0.560540:0.712708:0.556509:0.712708:0.000000
5:@0.564185:0.727866:0.579518:0.727866:0.579518:0.714150:0.564185:0.714150:0.000000
 1 que muestra  :@0.580126:0.728421:0.710357:0.728421:0.710357:0.712708:0.580126:0.712708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que      ( , 4, 1).:@0.073079:0.745062:0.196195:0.745062:0.196195:0.729350:0.073079:0.729350:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.117440:0.744773:0.132076:0.744773:0.132076:0.731363:0.117440:0.731363:0.000000
E:@0.135946:0.745062:0.144064:0.745062:0.144064:0.729627:0.135946:0.729627:0.000000
La pendiente de la recta tangente   a la elipse en el punto   está definida como: :@0.073089:0.774212:0.654426:0.774212:0.654426:0.758500:0.073089:0.758500:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.322286:0.774212:0.329907:0.774212:0.329907:0.758777:0.322286:0.758777:0.000000
m:@0.073089:0.808949:0.087704:0.808949:0.087704:0.793514:0.073089:0.793514:0.000000
     :@0.087630:0.808949:0.130059:0.808949:0.130059:0.793237:0.087630:0.793237:0.000000:0.000000:0.000000:0.000000:0.000000
5 2:@0.091588:0.808395:0.126120:0.808395:0.126120:0.794679:0.091588:0.794679:0.000000:0.000000:0.000000
a y:@0.134961:0.814400:0.167631:0.813992:0.167631:0.798557:0.134961:0.798964:0.000000:0.000000:0.000000
( ):@0.129286:0.815594:0.150234:0.815594:0.150234:0.782677:0.129286:0.782677:0.000000:0.000000:0.000000
b  x  :@0.135140:0.802467:0.177172:0.801159:0.177172:0.784321:0.135140:0.785628:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
₀ :@0.167629:0.814308:0.178252:0.814308:0.178252:0.797167:0.167629:0.797167:0.000000:0.000000
₀:@0.167333:0.801159:0.173558:0.801159:0.173558:0.784018:0.167333:0.784018:0.000000
:@0.149682:0.801886:0.155425:0.801886:0.155425:0.784744:0.149682:0.784744:0.000000
 , entonces       :@0.175253:0.808949:0.314584:0.808949:0.314584:0.793237:0.175253:0.793237:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.257614:0.808949:0.272229:0.808949:0.272229:0.793514:0.257614:0.793514:0.000000
5 2:@0.276113:0.808395:0.310645:0.808395:0.310645:0.794679:0.276113:0.794679:0.000000:0.000000:0.000000
4:@0.319486:0.816572:0.329285:0.816572:0.329285:0.799431:0.319486:0.799431:0.000000
( ):@0.313813:0.814910:0.334760:0.814910:0.334760:0.781994:0.313813:0.781994:0.000000:0.000000:0.000000
1 :@0.319666:0.801783:0.339948:0.801193:0.339948:0.784052:0.319666:0.784642:0.000000:0.000000:0.000000
3:@0.358290:0.819700:0.368089:0.819700:0.368089:0.802559:0.358290:0.802559:0.000000
2:@0.354290:0.833502:0.364090:0.833502:0.364090:0.816361:0.354290:0.816361:0.000000
2:@0.344227:0.801906:0.360954:0.801906:0.360954:0.786943:0.344227:0.786943:0.000000
2:@0.360955:0.802511:0.370755:0.802511:0.370755:0.785370:0.360955:0.785370:0.000000
     12:@0.374262:0.808949:0.434501:0.808949:0.434501:0.793237:0.374262:0.793237:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 2:@0.378211:0.808395:0.412743:0.808395:0.412743:0.794679:0.378211:0.794679:0.000000:0.000000:0.000000
La ecuación cartesiana de   es: :@0.073111:0.838100:0.298324:0.838100:0.298324:0.822388:0.073111:0.822388:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.263939:0.838100:0.271560:0.838100:0.271560:0.822665:0.263939:0.822665:0.000000
( ,  )     tal que     :@0.073111:0.873090:0.234019:0.873089:0.234019:0.857376:0.073111:0.857377:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.077915:0.873090:0.099838:0.873090:0.099838:0.857655:0.077915:0.857655:0.000000:0.000000:0.000000
[:@0.108502:0.872799:0.123138:0.872799:0.123138:0.859389:0.108502:0.859389:0.000000
R:@0.127008:0.872229:0.140298:0.872229:0.140298:0.859331:0.127008:0.859331:0.000000
2:@0.140199:0.867025:0.145436:0.867025:0.145436:0.857864:0.140199:0.857864:0.000000
y:@0.203389:0.873089:0.210863:0.873089:0.210863:0.857653:0.203389:0.857653:0.000000
1:@0.214747:0.872534:0.230080:0.872534:0.230080:0.858818:0.214747:0.858818:0.000000
3:@0.245497:0.867237:0.255296:0.867237:0.255296:0.850096:0.245497:0.850096:0.000000
2:@0.239949:0.881040:0.249749:0.881040:0.249749:0.863899:0.239949:0.863899:0.000000
   :@0.256715:0.873089:0.279938:0.873089:0.279938:0.857376:0.256715:0.857376:0.000000:0.000000:0.000000
5 2:@0.260666:0.872534:0.295198:0.872534:0.295198:0.858818:0.260666:0.858818:0.000000:0.000000:0.000000
3:@0.306666:0.866465:0.316465:0.866465:0.316465:0.849324:0.306666:0.849324:0.000000
12:@0.296594:0.880266:0.316192:0.880266:0.316192:0.863125:0.296594:0.863125:0.000000:0.000000
 (    2).:@0.317884:0.873089:0.374086:0.873089:0.374086:0.857376:0.317884:0.857376:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.326633:0.873089:0.334087:0.873089:0.334087:0.857653:0.326633:0.857653:0.000000
1:@0.337971:0.872534:0.353305:0.872534:0.353305:0.858818:0.337971:0.858818:0.000000
En la Figura 2.34. se muestran la elipse  ( , 4, 1), el punto :@0.073091:0.909798:0.481740:0.909803:0.481740:0.894090:0.073091:0.894085:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E:@0.352127:0.909798:0.360244:0.909798:0.360244:0.894362:0.352127:0.894362:0.000000
1:@0.481548:0.912226:0.487492:0.912226:0.487492:0.886547:0.481548:0.886547:0.000000
2 2:@0.487358:0.909248:0.533910:0.909248:0.533910:0.895533:0.487358:0.895533:0.000000:0.000000:0.000000
2,   :@0.502599:0.909803:0.537849:0.909803:0.537849:0.894090:0.502599:0.894090:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.549334:0.903145:0.559133:0.903145:0.559133:0.886004:0.549334:0.886004:0.000000
2:@0.543786:0.916947:0.553586:0.916947:0.553586:0.899806:0.543786:0.899806:0.000000
2:@0.560552:0.912226:0.566496:0.912226:0.566496:0.886547:0.560552:0.886547:0.000000
y la recta tangente.:@0.073089:0.938953:0.210968:0.938953:0.210968:0.923240:0.073089:0.923240:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.734802:0.309386:0.746269:0.309386:0.746269:0.299334:0.734802:0.299334:0.000000
 :@0.746269:0.310045:0.749201:0.310045:0.749201:0.298618:0.746269:0.298618:0.000000
Figura 2.33.:@0.749201:0.310045:0.809390:0.310045:0.809390:0.298618:0.749201:0.298618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.807646:0.287788:0.818797:0.287788:0.818797:0.277813:0.807646:0.277813:0.000000
b:@0.818797:0.288191:0.825531:0.288191:0.825531:0.276966:0.818797:0.276966:0.000000
b:@0.832184:0.155339:0.838918:0.155339:0.838918:0.144113:0.832184:0.144113:0.000000
L:@0.900552:0.277421:0.907480:0.277421:0.907480:0.263389:0.900552:0.263389:0.000000
L:@0.768572:0.284430:0.775500:0.284430:0.775500:0.270398:0.768572:0.270398:0.000000
4:@0.775500:0.287317:0.780261:0.287317:0.780261:0.278989:0.775500:0.278989:0.000000
L:@0.766901:0.197441:0.773828:0.197441:0.773828:0.183409:0.766901:0.183409:0.000000
2:@0.773827:0.200325:0.778588:0.200325:0.778588:0.191998:0.773827:0.191998:0.000000
L:@0.765227:0.158358:0.772155:0.158358:0.772155:0.144326:0.765227:0.144326:0.000000
1:@0.772153:0.161242:0.776914:0.161242:0.776914:0.152915:0.772153:0.152915:0.000000
L:@0.792080:0.143643:0.799008:0.143643:0.799008:0.129611:0.792080:0.129611:0.000000
3:@0.799008:0.146527:0.803769:0.146527:0.803769:0.138199:0.799008:0.138199:0.000000
a:@0.875853:0.231064:0.882587:0.231064:0.882587:0.219839:0.875853:0.219839:0.000000
2:@0.765088:0.230661:0.776240:0.230661:0.776240:0.220686:0.765088:0.220686:0.000000
a:@0.776240:0.231064:0.782973:0.231064:0.782973:0.219839:0.776240:0.219839:0.000000
0:@0.817333:0.230457:0.825091:0.230457:0.825091:0.216887:0.817333:0.216887:0.000000
y:@0.814726:0.141575:0.821721:0.141575:0.821721:0.128005:0.814726:0.128005:0.000000
x:@0.943302:0.231726:0.950122:0.231726:0.950122:0.218156:0.943302:0.218156:0.000000
u:@0.836897:0.207976:0.845660:0.207976:0.845660:0.193452:0.836897:0.193452:0.000000
:@0.839598:0.208484:0.845365:0.208484:0.845365:0.194209:0.839598:0.194209:0.000000
E 0 a b:@0.744742:0.264595:0.789697:0.264595:0.789697:0.251966:0.744742:0.251966:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( , ,  ):@0.751383:0.264595:0.793688:0.264595:0.793688:0.251739:0.751383:0.251739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.757438:0.263778:0.768838:0.265038:0.768838:0.252624:0.757438:0.251365:0.000000:0.000000:0.000000
Figura 2.34.:@0.861951:0.940006:0.922139:0.940006:0.922139:0.928578:0.861951:0.928578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.810519:0.901930:0.821671:0.901930:0.821671:0.891955:0.810519:0.891955:0.000000
1:@0.821671:0.902333:0.828203:0.902333:0.828203:0.890906:0.821671:0.890906:0.000000
1:@0.811188:0.860618:0.817721:0.860618:0.817721:0.849190:0.811188:0.849190:0.000000
L:@0.896717:0.919249:0.903645:0.919249:0.903645:0.905217:0.896717:0.905217:0.000000
4:@0.909502:0.895248:0.916034:0.895248:0.916034:0.883821:0.909502:0.883821:0.000000
2:@0.743997:0.894845:0.755148:0.894845:0.755148:0.884870:0.743997:0.884870:0.000000
2:@0.755148:0.895248:0.761681:0.895248:0.761681:0.883821:0.755148:0.883821:0.000000
2:@0.690703:0.894845:0.701854:0.894845:0.701854:0.884870:0.690703:0.884870:0.000000
4:@0.701854:0.895248:0.708387:0.895248:0.708387:0.883821:0.701854:0.883821:0.000000
0:@0.799478:0.894640:0.807236:0.894640:0.807236:0.881070:0.799478:0.881070:0.000000
y:@0.793517:0.836240:0.800511:0.836240:0.800511:0.822670:0.793517:0.822670:0.000000
x:@0.918755:0.895897:0.925574:0.895897:0.925574:0.882327:0.918755:0.882327:0.000000
E 0:@0.866994:0.863677:0.884585:0.863677:0.884585:0.851048:0.866994:0.851048:0.000000:0.000000:0.000000
( , 4, 1):@0.873636:0.863677:0.915700:0.863677:0.915700:0.850821:0.873636:0.850821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.879690:0.862860:0.891091:0.864120:0.891091:0.851706:0.879690:0.850447:0.000000:0.000000:0.000000
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