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Ejercicios sobre la hipérbola

Clase 194. Ejercicios sobre la hipérbola. c. e =. a. Ecuación canónica. triángulo característico. y. c 2 = a 2 + b 2. x. excentricidad. > 1. y 2. asíntotas. x 2. = 1. b. y = ± x. a 2. b 2. a. (y – k) 2. (x – h) 2. = 1. a 2. b 2. (y – k) 2. (x – h) 2. = 1. a 2.

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Ejercicios sobre la hipérbola

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  1. Clase 194 Ejercicios sobre la hipérbola

  2. c e = a Ecuación canónica triángulo característico y c2= a2+ b2 x excentricidad > 1 y2 asíntotas x2 = 1 b y = ± x a2 b2 a

  3. (y – k)2 (x – h)2 = 1 a2 b2 (y – k)2 (x – h)2 = 1 a2 b2 Ecuación de la hipérbola con centro O(h;k) Eje principal paralelo al eje x Eje principal paralelo al eje y

  4. Ejercicio 1 Escribe la ecuación y representa gráficamente la hipérbola que cumple: O(4;3) , A2(8;3) y e = 1,25

  5. c e = a (y – )2 (x – )2 3 k h O(4;3) , A2(8;3) , e = 1,25 4 = 1 a2 b2 9 16 Hipérbola de eje principal paralelo al eje x. a = d(O;A2) = 4 c2= a2+ b2 c = e· a b2= c2 – a2 c = 1,25·4 b2= 25 – 16 c = 5 b2= 9 b = 3

  6. 3 3 y = x y =– x + 6 4 4 O(4;3), A2(8;3), a = 4, b = 3, c = 5 y A1(0;3) F1( –1;3) O 3 F2(9;3) F1 F2 A1 A2 –1 9 x 0 4 8

  7. Ejercicio 2 Representa gráficamente la hipérbola de ecuación 4x2 –9y2 –24x –36y –144 = 0

  8. (x –3)2 (y +2)2 = 1 36 16 Eje principal paralelo al eje x c2= a2 + b2 O (3; –2) c2=36 +16 a2= 36 c2=52 a = 6u c =√52  7,2u b2= 16 A1( ; –2) A2( ; –2) 9 –3 b = 4u F1( ; –2) F2( ; –2) –4,2 10,2

  9. ; a = 6u ; b = 4u O (3; –2) ; c =7,2u y 2 –4,2 –3 3 9 10,2 0 x A2 A1 F1 F2 –2 O –6

  10. b y – yO m =  m = a x – xO y + 2 2 = 3 x – 3 y + 2 2 = 3 x – 3 4 2 asíntotas =  6 3 2x – 6 = 3y + 6 –2x + 6 = 3y + 6 2x + 3y = 0 2x – 3y –12 = 0

  11. Para el estudio individual Representa gráficamente la hipérbola de ecuación 9y2 –16x2 +160x +72y – 400= 0

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