1 / 11

La elipse

Clase 185. La elipse. (continuación). Ecuación canónica. y. Eje mayor en el eje. B 1. y. P. x. y. A 1. x. A 2. x. O. F 2. F 1. y 2. x 2. B 2. +. = 1. a 2. b 2. c. e =. a. Relaciones métricas en la elipse. y. B 1. a. b. c. A 2. F 2. O. A 1. F 1. x. B 2.

speranza-arkins
Download Presentation

La elipse

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Clase 185 La elipse (continuación)

  2. Ecuación canónica y Eje mayor en el eje B1 y P x y A1 x A2 x O F2 F1 y2 x2 B2 + = 1 a2 b2

  3. c e = a Relaciones métricas en la elipse y B1 a b c A2 F2 O A1 F1 x B2 Triángulo característico excentricidad a2 = b2 + c2 < 1

  4. y2 x2 + = 1 a2 b2 Eje mayor paralelo al eje y x y O k F2 F1 x h (x – h)2 (y – k)2 + = 1 b2 a2

  5. c e = a Ejercicio 1 Escribe la ecuación de la elipse que cumple: O(3;2) , a = 13 , e = 0,923 a2= b2 + c2 b2= a2 – c2 c = e · a b2= 132 – 122 c = 0,923 · 13 c = 11,999 b2= 169 – 144 c ≈ 12 b2= 25

  6. O(3;2) , a = 13 , b2 = 25 Con eje mayor paralelo al eje x (x – )2 (y – )2 2 k 3 h + = 1 a2 b2 25 169 Con eje mayor paralelo al eje y (x – )2 3 2 (y – )2 k h + = 1 25 a2 b2 169

  7. Ejercicio 2 Determina centro, vértices, focos y representa gráficamente la elipse: 9x2+25y2–72x–150y+144 = 0

  8. (y – 3)2 (x – 4)2 + 25 9 9x2+25y2–72x–150y+144 = 0 9x2–72x+25y2–150y+144 = 0 9(x2–8x) +25(y2–6y) = –144 = 0 = 225 9(x2–8x+16) +25(y2–6y+9) + 25(y – 3)2 = 225 9(x – 4)2 = 1 Elipse de centro O(4;3) y eje mayor paralelo al eje x.

  9. O(4;3) A1( ; 3) –1 a2= 25 b2= 9 A2( ; 3) 9 b = 3 a = 5 0 F1( ; 3) a2= b2 + c2 F2( ; 3) 8 c2= a2– b2 B1(4 ; ) 6 c2= 25– 9 c2= 16 B2(4 ; ) 0 c = 4

  10. y B1 6 3 O A1 A2 F1 F2 B2 x –1 8 9 0 4

  11. Para el estudio individual 1. Representa en un sistema de coordenadas la elipse 9x2 + y2 – 8y + 7 = 0 2. Resuelve la siguiente ecuación sabiendo que: 0 < x < 3600 cos2x – 0,5 cosx + sen2x = 0 Resp: 600; 3000

More Related