All ellipses $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ $(0 < b < a)$ have fixed major axis. Tangent at any end points of a latus rectum meet at a fixed point which can be

(a, a)

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(0, a)

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(0, - a)

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(0, 0)

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Solution

The correct options are
B $(0, a)$
C $(0, - a)$
$C o - o r d i n a t e s o f l a t u s r e c t u m : (a e, \frac{b^{2}}{a}) E q u a t i o n o f t a n g e n t : \frac{x e}{a} + \frac{y}{a} = 1 O r, x e + (y - a) = 0 W e k n o w, L 1 + λ L 2 = 0 T h e n b o t h p a s s e s t h r o u g h a f i x e d w h i c h i s : x = 0 a n d y - a = 0 O r, y = a (0, a) C o - o r d i n a t e s o f l a t u s r e c t u m : (a e, - \frac{b^{2}}{a}) E q u a t i o n o f t a n g e n t : \frac{x e}{a} - \frac{y}{a} = 1 O r, x e - (y + a) = 0 W e k n o w, L 1 + λ L 2 = 0 T h e n b o t h p a s s e s t h r o u g h a f i x e d w h i c h i s : x = 0 a n d y + a = 0 O r, y = - a (0, - a)$

Option [B][C]

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