122:@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 Ejercicio resuelto:@0.293660:0.136836:0.422242:0.136836:0.422242:0.120167:0.293660:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Los focos de una elipse ( , , ) son ( 4, 0), (4, 0), y los vértices son ( 5, 0), (5, :@0.293660:0.172783:0.930993:0.172776:0.930993:0.157064:0.293660:0.157070:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 E:@0.464074:0.172783:0.472192:0.172783:0.472192:0.157347:0.464074:0.157347:0.000000 a b:@0.491167:0.172776:0.516440:0.172776:0.516440:0.157341:0.491167:0.157341:0.000000:0.000000:0.000000 1:@0.563182:0.175949:0.568419:0.175949:0.568419:0.166788:0.563182:0.166788:0.000000 5 2:@0.572092:0.172222:0.611170:0.172222:0.611170:0.158506:0.572092:0.158506:0.000000:0.000000:0.000000 2:@0.659357:0.175949:0.664594:0.175949:0.664594:0.166788:0.659357:0.166788:0.000000 5:@0.668266:0.172222:0.683599:0.172222:0.683599:0.158506:0.668266:0.158506:0.000000 2:@0.858487:0.172222:0.873820:0.172222:0.873820:0.158506:0.858487:0.158506:0.000000 0). Mostrar que la elipse es::@0.293660:0.189418:0.487409:0.189418:0.487409:0.173705:0.293660:0.173705:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 E:@0.448999:0.230468:0.457117:0.230468:0.457117:0.215033:0.448999:0.215033:0.000000 ( , 5, 3) ( , ) | :@0.457043:0.230468:0.648289:0.230467:0.648289:0.214754:0.457043:0.214755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.509955:0.229912:0.525289:0.229912:0.525289:0.216196:0.509955:0.216196:0.000000 5:@0.529367:0.235637:0.533453:0.235637:0.533453:0.212355:0.529367:0.212355:0.000000 5:@0.544981:0.229912:0.560314:0.229912:0.560314:0.216196:0.544981:0.216196:0.000000 x y:@0.568966:0.230467:0.590889:0.230467:0.590889:0.215031:0.568966:0.215031:0.000000:0.000000:0.000000 [:@0.599585:0.230177:0.614222:0.230177:0.614222:0.216767:0.599585:0.216767:0.000000 R:@0.618091:0.229607:0.631381:0.229607:0.631381:0.216709:0.618091:0.216709:0.000000 2:@0.631283:0.224403:0.636519:0.224403:0.636519:0.215242:0.631283:0.215242:0.000000 5:@0.654581:0.237870:0.664381:0.237870:0.664381:0.220729:0.654581:0.220729:0.000000 ( ) ( ):@0.647411:0.237307:0.725924:0.237454:0.725924:0.204537:0.647411:0.204391:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.656855:0.222781:0.668602:0.222781:0.668602:0.205943:0.656855:0.205943:0.000000:0.000000 :@0.672378:0.222872:0.678121:0.222872:0.678121:0.205731:0.672378:0.205731:0.000000 :@0.678218:0.230467:0.701441:0.230467:0.701441:0.214754:0.678218:0.214754:0.000000:0.000000:0.000000 1:@0.682169:0.229912:0.697502:0.229912:0.697502:0.216196:0.682169:0.216196:0.000000 3:@0.707746:0.238075:0.717546:0.238075:0.717546:0.220934:0.707746:0.220934:0.000000 y:@0.709037:0.221319:0.717189:0.221319:0.717189:0.204480:0.709037:0.204480:0.000000 :@0.725543:0.223074:0.731286:0.223074:0.731286:0.205933:0.725543:0.205933:0.000000 1 .:@0.731385:0.230467:0.771571:0.230467:0.771571:0.214754:0.731385:0.214754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.735335:0.229912:0.750669:0.229912:0.750669:0.216196:0.735335:0.216196:0.000000 6:@0.763649:0.234263:0.767736:0.234263:0.767736:0.210981:0.763649:0.210981:0.000000 En primer lugar, de las coordenadas de los focos se obtiene 4, y de las coordenadas :@0.293660:0.266408:0.931022:0.266408:0.931022:0.250695:0.293660:0.250695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c:@0.727206:0.266408:0.734864:0.266408:0.734864:0.250973:0.727206:0.250973:0.000000 5:@0.738876:0.265853:0.754210:0.265853:0.754210:0.252138:0.738876:0.252138:0.000000 de los vértices, 5. Como , entonces, :@0.293642:0.283050:0.669806:0.283050:0.669806:0.267337:0.293642:0.267337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.403423:0.283050:0.412681:0.283050:0.412681:0.267615:0.403423:0.267615:0.000000 5:@0.416565:0.282495:0.431899:0.282495:0.431899:0.268779:0.416565:0.268779:0.000000 c:@0.500410:0.283050:0.508068:0.283050:0.508068:0.267615:0.500410:0.267615:0.000000 2:@0.508018:0.276986:0.513254:0.276986:0.513254:0.267825:0.508018:0.267825:0.000000 5:@0.517166:0.282495:0.532499:0.282495:0.532499:0.268779:0.517166:0.268779:0.000000 a:@0.536365:0.283050:0.545624:0.283050:0.545624:0.267615:0.536365:0.267615:0.000000 2:@0.545543:0.276986:0.550780:0.276986:0.550780:0.267825:0.545543:0.267825:0.000000 2:@0.554690:0.282495:0.570023:0.282495:0.570023:0.268779:0.554690:0.268779:0.000000 b:@0.573889:0.283050:0.583148:0.283050:0.583148:0.267615:0.573889:0.267615:0.000000 2:@0.583067:0.276986:0.588304:0.276986:0.588304:0.267825:0.583067:0.267825:0.000000 b:@0.511885:0.318996:0.521144:0.318996:0.521144:0.303561:0.511885:0.303561:0.000000 2:@0.521078:0.312926:0.526315:0.312926:0.526315:0.303766:0.521078:0.303766:0.000000 , 25 16 9,:@0.526268:0.318990:0.708687:0.318990:0.708687:0.303277:0.526268:0.303277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.530225:0.318435:0.545558:0.318435:0.545558:0.304720:0.530225:0.304720:0.000000 a:@0.549424:0.318990:0.558683:0.318990:0.558683:0.303555:0.549424:0.303555:0.000000 2:@0.558602:0.312926:0.563839:0.312926:0.563839:0.303766:0.558602:0.303766:0.000000 2:@0.567751:0.318435:0.583084:0.318435:0.583084:0.304720:0.567751:0.304720:0.000000 c:@0.586950:0.318990:0.594607:0.318990:0.594607:0.303555:0.586950:0.303555:0.000000 2:@0.594525:0.312926:0.599762:0.312926:0.599762:0.303766:0.594525:0.303766:0.000000 2:@0.636438:0.318435:0.651772:0.318435:0.651772:0.304720:0.636438:0.304720:0.000000 5:@0.677376:0.318435:0.692709:0.318435:0.692709:0.304720:0.677376:0.304720:0.000000 donde 3. La ecuación cartesiana de la elipse es::@0.293640:0.354936:0.677947:0.354936:0.677947:0.339224:0.293640:0.339224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b:@0.345806:0.354936:0.355065:0.354936:0.355065:0.339501:0.345806:0.339501:0.000000 5:@0.358949:0.354382:0.374282:0.354382:0.374282:0.340666:0.358949:0.340666:0.000000 E:@0.647096:0.354936:0.655214:0.354936:0.655214:0.339501:0.647096:0.339501:0.000000 ( , ) tal que :@0.485904:0.396042:0.616351:0.396030:0.616351:0.380318:0.485904:0.380329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.490708:0.396042:0.512631:0.396042:0.512631:0.380606:0.490708:0.380606:0.000000:0.000000:0.000000 [:@0.521334:0.395740:0.535971:0.395740:0.535971:0.382330:0.521334:0.382330:0.000000 R:@0.539840:0.395170:0.553130:0.395170:0.553130:0.382273:0.539840:0.382273:0.000000 2:@0.553032:0.389966:0.558269:0.389966:0.558269:0.380806:0.553032:0.380806:0.000000 5:@0.622599:0.404747:0.632399:0.404747:0.632399:0.387606:0.622599:0.387606:0.000000 ( ) ( ):@0.615431:0.404185:0.693943:0.402760:0.693943:0.369844:0.615431:0.371268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.624875:0.389658:0.636622:0.389658:0.636622:0.372820:0.624875:0.372820:0.000000:0.000000 :@0.640398:0.389749:0.646141:0.389749:0.646141:0.372608:0.640398:0.372608:0.000000 :@0.646238:0.396030:0.669459:0.396030:0.669459:0.380318:0.646238:0.380318:0.000000:0.000000:0.000000 1:@0.650187:0.395476:0.665520:0.395476:0.665520:0.381760:0.650187:0.381760:0.000000 3:@0.675766:0.403382:0.685566:0.403382:0.685566:0.386241:0.675766:0.386241:0.000000 y:@0.677056:0.386625:0.685209:0.386625:0.685209:0.369787:0.677056:0.369787:0.000000 :@0.693563:0.388380:0.699306:0.388380:0.699306:0.371239:0.693563:0.371239:0.000000 1.:@0.699403:0.396030:0.734664:0.396030:0.734664:0.380318:0.699403:0.380318:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.703354:0.395476:0.718687:0.395476:0.718687:0.381760:0.703354:0.381760:0.000000 Calculamos la excentricidad: .:@0.293663:0.434653:0.584393:0.434657:0.584393:0.418944:0.293663:0.418941:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 e:@0.502696:0.434653:0.510483:0.434653:0.510483:0.419218:0.502696:0.419218:0.000000 5:@0.514366:0.434098:0.529700:0.434098:0.529700:0.420383:0.514366:0.420383:0.000000 a:@0.533950:0.441334:0.543209:0.441334:0.543209:0.425899:0.533950:0.425899:0.000000 c :@0.534310:0.427118:0.546278:0.427118:0.546278:0.410279:0.534310:0.410279:0.000000:0.000000 5:@0.549749:0.434102:0.565082:0.434102:0.565082:0.420387:0.549749:0.420387:0.000000 5:@0.569901:0.442080:0.579700:0.442080:0.579700:0.424939:0.569901:0.424939:0.000000 4:@0.570201:0.428361:0.580000:0.428361:0.580000:0.411220:0.570201:0.411220:0.000000 5.2 Problemas relativos a la elipse:@0.293660:0.470597:0.557258:0.470597:0.557258:0.453650:0.293660:0.453650:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5.2.1 Ecuación cartesiana de la recta tangente a una elipse:@0.293660:0.506543:0.732217:0.506543:0.732217:0.489874:0.293660:0.489874:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Tratamos el problema de hallar la ecuación vectorial o cartesiana de la recta :@0.341096:0.542490:0.930669:0.542490:0.930669:0.526777:0.341096:0.526777:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tangente a una elipse en un punto dado de esta. Para el efecto, supongamos :@0.341096:0.559132:0.930593:0.559132:0.930593:0.543419:0.341096:0.543419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 conocida la elipse ( , , ), donde , :@0.341096:0.575773:0.662418:0.575761:0.662418:0.560048:0.341096:0.560061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 E:@0.483586:0.575773:0.491704:0.575773:0.491704:0.560338:0.483586:0.560338:0.000000 a b:@0.513511:0.575761:0.541085:0.575761:0.541085:0.560326:0.513511:0.560326:0.000000:0.000000:0.000000 a b:@0.610278:0.575761:0.637852:0.575761:0.637852:0.560326:0.610278:0.560326:0.000000:0.000000:0.000000 [:@0.643552:0.575471:0.658188:0.575471:0.658188:0.562061:0.643552:0.562061:0.000000 R:@0.663927:0.574901:0.677217:0.574901:0.677217:0.562004:0.663927:0.562004:0.000000 1:@0.677418:0.569374:0.686357:0.569374:0.686357:0.561377:0.677418:0.561377:0.000000 , y un punto de esta ( , ) :@0.686478:0.575761:0.930943:0.575761:0.930943:0.560048:0.686478:0.560048:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.861065:0.575206:0.876399:0.575206:0.876399:0.561490:0.861065:0.561490:0.000000 x y:@0.887185:0.575761:0.916531:0.575761:0.916531:0.560326:0.887185:0.560326:0.000000:0.000000:0.000000 0:@0.894806:0.578933:0.900043:0.578933:0.900043:0.569773:0.894806:0.569773:0.000000 0:@0.916690:0.578933:0.921927:0.578933:0.921927:0.569773:0.916690:0.569773:0.000000 :@0.926911:0.575761:0.930943:0.575761:0.930943:0.560048:0.926911:0.560048:0.000000 [:@0.341094:0.592113:0.355730:0.592113:0.355730:0.578703:0.341094:0.578703:0.000000 ( , , ).:@0.355642:0.592403:0.420369:0.592403:0.420369:0.576690:0.355642:0.576690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 E:@0.359600:0.592403:0.367718:0.592403:0.367718:0.576967:0.359600:0.576967:0.000000 a b:@0.386923:0.592403:0.412435:0.592403:0.412435:0.576967:0.386923:0.576967:0.000000:0.000000:0.000000 Buscamos una recta tangente a ( , , ) en el punto ( , ) ( , , ). :@0.341071:0.628349:0.930956:0.628343:0.930956:0.612630:0.341071:0.612636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 L:@0.497661:0.628349:0.505282:0.628349:0.505282:0.612914:0.497661:0.612914:0.000000 E:@0.597798:0.628349:0.605916:0.628349:0.605916:0.612914:0.597798:0.612914:0.000000 a b:@0.627223:0.628343:0.654411:0.628343:0.654411:0.612907:0.627223:0.612907:0.000000:0.000000:0.000000 5:@0.771762:0.627788:0.787095:0.627788:0.787095:0.614072:0.771762:0.614072:0.000000 x y:@0.797477:0.628343:0.826378:0.628343:0.826378:0.612907:0.797477:0.612907:0.000000:0.000000:0.000000 0:@0.805032:0.631515:0.810269:0.631515:0.810269:0.622355:0.805032:0.622355:0.000000 0:@0.826476:0.631515:0.831713:0.631515:0.831713:0.622355:0.826476:0.622355:0.000000 [:@0.842016:0.628053:0.856652:0.628053:0.856652:0.614643:0.842016:0.614643:0.000000 E:@0.862004:0.628343:0.870122:0.628343:0.870122:0.612907:0.862004:0.612907:0.000000 a b:@0.891417:0.628343:0.918605:0.628343:0.918605:0.612907:0.891417:0.612907:0.000000:0.000000:0.000000 Más aún, buscamos la ecuación cartesiana o vectorial de dicha tangente . Esto :@0.341114:0.644985:0.930956:0.644985:0.930956:0.629272:0.341114:0.629272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 L:@0.880649:0.644985:0.888270:0.644985:0.888270:0.629549:0.880649:0.629549:0.000000 nos conduce a considerar dos casos.:@0.341114:0.661626:0.604929:0.661626:0.604929:0.645914:0.341114:0.645914:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En el primero, la recta tangente a la elipse ( , , ) en el punto (:@0.341114:0.697573:0.860120:0.697566:0.860120:0.681854:0.341114:0.681860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 L:@0.578144:0.697573:0.585765:0.697573:0.585765:0.682137:0.578144:0.682137:0.000000 E:@0.667603:0.697573:0.675721:0.697573:0.675721:0.682137:0.667603:0.682137:0.000000 a b:@0.695956:0.697566:0.722315:0.697566:0.722315:0.682131:0.695956:0.682131:0.000000:0.000000:0.000000 5 2:@0.835289:0.697012:0.875490:0.697012:0.875490:0.683296:0.835289:0.683296:0.000000:0.000000:0.000000 a:@0.875527:0.697566:0.884786:0.697566:0.884786:0.682131:0.875527:0.682131:0.000000 , 0) es :@0.884804:0.697566:0.930933:0.697566:0.930933:0.681854:0.884804:0.681854:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 paralela al eje . Observamos que, en este caso, no está definida la pendiente de :@0.341109:0.714208:0.931021:0.714208:0.931021:0.698496:0.341109:0.698496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.444963:0.714208:0.452418:0.714208:0.452418:0.698773:0.444963:0.698773:0.000000 dicha recta. La ecuación vectorial de esta recta está definida como::@0.341109:0.730850:0.823679:0.730850:0.823679:0.715137:0.341109:0.715137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.533160:0.766791:0.548137:0.766791:0.548137:0.751079:0.533160:0.751079:0.000000:0.000000:0.000000 t:@0.537958:0.766791:0.543333:0.766791:0.543333:0.751356:0.537958:0.751356:0.000000 5 2:@0.552003:0.766237:0.591320:0.766237:0.591320:0.752521:0.552003:0.752521:0.000000:0.000000:0.000000 (:@0.567244:0.766791:0.576079:0.766791:0.576079:0.751079:0.567244:0.751079:0.000000:0.000000 a:@0.591228:0.766791:0.600487:0.766791:0.600487:0.751356:0.591228:0.751356:0.000000 , 0) (0, 1), .:@0.600414:0.766791:0.743269:0.766791:0.743269:0.751079:0.600414:0.751079:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.625135:0.766237:0.640468:0.766237:0.640468:0.752521:0.625135:0.752521:0.000000 t:@0.644333:0.766791:0.649708:0.766791:0.649708:0.751356:0.644333:0.751356:0.000000 t:@0.699077:0.766791:0.704451:0.766791:0.704451:0.751356:0.699077:0.751356:0.000000 [:@0.708362:0.766501:0.722998:0.766501:0.722998:0.753092:0.708362:0.753092:0.000000 R:@0.726868:0.765932:0.740158:0.765932:0.740158:0.753034:0.726868:0.753034:0.000000 En la Figura 2.31. se muestra la recta tangente a la elipse ( , , ) en el punto :@0.341107:0.802738:0.918460:0.802731:0.918460:0.787019:0.341107:0.787025:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 L:@0.679101:0.802738:0.686722:0.802738:0.686722:0.787302:0.679101:0.787302:0.000000 E:@0.766738:0.802738:0.774856:0.802738:0.774856:0.787302:0.766738:0.787302:0.000000 a b:@0.794501:0.802731:0.820456:0.802731:0.820456:0.787296:0.794501:0.787296:0.000000:0.000000:0.000000 5 2:@0.341094:0.818819:0.380412:0.818819:0.380412:0.805103:0.341094:0.805103:0.000000:0.000000:0.000000 (:@0.356335:0.819373:0.365171:0.819373:0.365171:0.803661:0.356335:0.803661:0.000000:0.000000 a:@0.380320:0.819373:0.389579:0.819373:0.389579:0.803938:0.380320:0.803938:0.000000 , 0). Se tiene ( , , ) { }.:@0.389505:0.819373:0.612490:0.819373:0.612490:0.803661:0.389505:0.803661:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 E:@0.479498:0.819373:0.487616:0.819373:0.487616:0.803938:0.479498:0.803938:0.000000 a b:@0.506843:0.819373:0.532355:0.819373:0.532355:0.803938:0.506843:0.803938:0.000000:0.000000:0.000000 >:@0.541025:0.819235:0.556358:0.819235:0.556358:0.805186:0.541025:0.805186:0.000000 L:@0.560224:0.819373:0.567845:0.819373:0.567845:0.803938:0.560224:0.803938:0.000000 5:@0.571728:0.818819:0.587062:0.818819:0.587062:0.805103:0.571728:0.805103:0.000000 De manera similar, tratamos el caso de la recta tangente a ( , , ) en el punto :@0.341094:0.855313:0.930948:0.855313:0.930948:0.839601:0.341094:0.839601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 L E:@0.754502:0.855313:0.787194:0.855313:0.787194:0.839878:0.754502:0.839878:0.000000:0.000000:0.000000 a b:@0.806864:0.855313:0.832819:0.855313:0.832819:0.839878:0.806864:0.839878:0.000000:0.000000:0.000000 (:@0.349109:0.871955:0.377135:0.871955:0.377135:0.856243:0.349109:0.856243:0.000000:0.000000:0.000000:0.000000 5 2:@0.353059:0.871400:0.392377:0.871400:0.392377:0.857685:0.353059:0.857685:0.000000:0.000000:0.000000 a:@0.392285:0.871955:0.401543:0.871955:0.401543:0.856520:0.392285:0.856520:0.000000 , 0).:@0.401470:0.871955:0.425473:0.871955:0.425473:0.856243:0.401470:0.856243:0.000000:0.000000:0.000000:0.000000:0.000000 En el segundo caso, suponemos que ( , ) ( , , ) con ≠ ± exactamente :@0.341076:0.907902:0.930944:0.907895:0.930944:0.892182:0.341076:0.892189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.618565:0.907902:0.646147:0.907895:0.646147:0.892460:0.618565:0.892466:0.000000:0.000000:0.000000 0:@0.625985:0.911067:0.631222:0.911067:0.631222:0.901907:0.625985:0.901907:0.000000 0:@0.646099:0.911067:0.651336:0.911067:0.651336:0.901907:0.646099:0.901907:0.000000 [:@0.660470:0.907605:0.675106:0.907605:0.675106:0.894195:0.660470:0.894195:0.000000 E:@0.679392:0.907895:0.687510:0.907895:0.687510:0.892460:0.679392:0.892460:0.000000 a b:@0.707186:0.907895:0.733140:0.907895:0.733140:0.892460:0.707186:0.892460:0.000000:0.000000:0.000000 x:@0.774280:0.907895:0.781735:0.907895:0.781735:0.892460:0.774280:0.892460:0.000000 a,:@0.812218:0.907895:0.824753:0.907895:0.824753:0.892460:0.812218:0.892460:0.000000:0.000000 2:@0.341102:0.923982:0.356436:0.923982:0.356436:0.910267:0.341102:0.910267:0.000000 a x:@0.356159:0.924537:0.391078:0.924537:0.391078:0.909102:0.356159:0.909102:0.000000:0.000000:0.000000 < < . En la Figura 2.32. se muestra la recta tangente a la elipse en el punto :@0.365161:0.924537:0.931047:0.924537:0.931047:0.908824:0.365161:0.908824:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.390819:0.927709:0.396055:0.927709:0.396055:0.918549:0.390819:0.918549:0.000000 a:@0.414363:0.924537:0.423622:0.924537:0.423622:0.909102:0.414363:0.909102:0.000000 L:@0.756333:0.924537:0.763954:0.924537:0.763954:0.909102:0.756333:0.909102:0.000000 :@0.926895:0.924537:0.930926:0.924537:0.930926:0.908824:0.926895:0.908824:0.000000 ( , ) ( , , ).:@0.349109:0.941179:0.497318:0.941179:0.497318:0.925466:0.349109:0.925466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.353059:0.940624:0.368392:0.940624:0.368392:0.926908:0.353059:0.926908:0.000000 x y:@0.377043:0.941179:0.404169:0.941179:0.404169:0.925744:0.377043:0.925744:0.000000:0.000000:0.000000 0:@0.384436:0.944351:0.389673:0.944351:0.389673:0.935191:0.384436:0.935191:0.000000 0:@0.404105:0.944351:0.409342:0.944351:0.409342:0.935191:0.404105:0.935191:0.000000 [:@0.418043:0.940889:0.432679:0.940889:0.432679:0.927479:0.418043:0.927479:0.000000 E:@0.436549:0.941179:0.444667:0.941179:0.444667:0.925744:0.436549:0.925744:0.000000 a b:@0.463872:0.941179:0.489384:0.941179:0.489384:0.925744:0.463872:0.925744:0.000000:0.000000:0.000000 Figura 2.31.:@0.073230:0.727468:0.133419:0.727468:0.133419:0.716040:0.073230:0.716040:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Figura 2.32.:@0.073230:0.940009:0.133419:0.940009:0.133419:0.928582:0.073230:0.928582:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.155114:0.697908:0.166265:0.697908:0.166265:0.687933:0.155114:0.687933:0.000000 b:@0.166265:0.698312:0.172999:0.698312:0.172999:0.687086:0.166265:0.687086:0.000000 b:@0.164592:0.558308:0.171326:0.558308:0.171326:0.547083:0.164592:0.547083:0.000000 L:@0.120124:0.569731:0.126359:0.569731:0.126359:0.557102:0.120124:0.557102:0.000000 E 0 a b:@0.213936:0.579364:0.259102:0.579364:0.259102:0.566735:0.213936:0.566735:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( , , ):@0.220577:0.579364:0.263093:0.579364:0.263093:0.566508:0.220577:0.566508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000  :@0.226632:0.578547:0.238032:0.579807:0.238032:0.567393:0.226632:0.566134:0.000000:0.000000:0.000000 a:@0.224994:0.637610:0.231728:0.637610:0.231728:0.626385:0.224994:0.626385:0.000000 2:@0.112556:0.637207:0.123708:0.637207:0.123708:0.627232:0.112556:0.627232:0.000000 a:@0.123708:0.637610:0.130441:0.637610:0.130441:0.626385:0.123708:0.626385:0.000000 0:@0.164801:0.637003:0.172559:0.637003:0.172559:0.623433:0.164801:0.623433:0.000000 y:@0.162194:0.542659:0.169189:0.542659:0.169189:0.529089:0.162194:0.529089:0.000000 x:@0.282408:0.638272:0.289228:0.638272:0.289228:0.624702:0.282408:0.624702:0.000000 u:@0.147182:0.620919:0.154802:0.620919:0.154802:0.608291:0.147182:0.608291:0.000000 :@0.149531:0.621362:0.154546:0.621362:0.154546:0.608949:0.149531:0.608949:0.000000 2:@0.140769:0.922202:0.151921:0.922202:0.151921:0.912227:0.140769:0.912227:0.000000 b:@0.151919:0.922606:0.158653:0.922606:0.158653:0.911380:0.151919:0.911380:0.000000 b:@0.150246:0.796894:0.156980:0.796894:0.156980:0.785668:0.150246:0.785668:0.000000 L:@0.230232:0.906971:0.237160:0.906971:0.237160:0.892939:0.230232:0.892939:0.000000 E 0 a b:@0.194922:0.799911:0.240088:0.799911:0.240088:0.787282:0.194922:0.787282:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( , , ) { }:@0.201564:0.799911:0.302551:0.799911:0.302551:0.787055:0.201564:0.787055:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000  :@0.207618:0.799094:0.219019:0.800354:0.219019:0.787940:0.207618:0.786681:0.000000:0.000000:0.000000 >:@0.247378:0.799495:0.258529:0.799495:0.258529:0.789278:0.247378:0.789278:0.000000 L:@0.261827:0.799911:0.268062:0.799911:0.268062:0.787282:0.261827:0.787282:0.000000 5:@0.271361:0.799457:0.283906:0.799457:0.283906:0.788235:0.271361:0.788235:0.000000 u:@0.291195:0.799911:0.298816:0.799911:0.298816:0.787282:0.291195:0.787282:0.000000 :@0.292792:0.800354:0.297807:0.800354:0.297807:0.787940:0.292792:0.787940:0.000000 a:@0.208977:0.869053:0.215710:0.869053:0.215710:0.857827:0.208977:0.857827:0.000000 2:@0.098212:0.868650:0.109363:0.868650:0.109363:0.858675:0.098212:0.858675:0.000000 a:@0.109363:0.869053:0.116097:0.869053:0.116097:0.857827:0.109363:0.857827:0.000000 0:@0.150455:0.868444:0.158213:0.868444:0.158213:0.854874:0.150455:0.854874:0.000000 y:@0.147848:0.781658:0.154843:0.781658:0.154843:0.768088:0.147848:0.768088:0.000000 x:@0.268062:0.869702:0.274882:0.869702:0.274882:0.856132:0.268062:0.856132:0.000000 u:@0.175039:0.842182:0.183802:0.842182:0.183802:0.827659:0.175039:0.827659:0.000000 :@0.177741:0.842691:0.183509:0.842691:0.183509:0.828416:0.177741:0.828416:0.000000 E 0 a b:@0.079538:0.903844:0.124704:0.903844:0.124704:0.891215:0.079538:0.891215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( , , ):@0.086179:0.903844:0.128695:0.903844:0.128695:0.890989:0.086179:0.890989:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000  :@0.092234:0.903027:0.103635:0.904287:0.103635:0.891874:0.092234:0.890614:0.000000:0.000000:0.000000 DBA 5 (Ev. 3) Utiliza las expresiones simbólicas de las cónicas y propone los rangos de variación para obtener una gráfica requerida.:@0.230560:0.971366:0.917487:0.971366:0.917487:0.959939:0.230560:0.959939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@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