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Q.

Semi transverse axes of hyperbola is 5. Tangent at the point P and normal to this tangent meet conjugate axes at A and B. the circle on AB as diameter passes through two fixed points, distance between them is 20. Then eccentricity is

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answer is 2.

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Detailed Solution

Let $P = (asec θ, btan θ)$ and given a=5

equation of tangent is $\frac{x}{a} \sec θ - \frac{y}{b} \tan θ = 1$ and normal is
$\begin{array}{l} axcos θ + bycot θ = a^{2} e^{2} \\ A (o, - bcot θ) \\ B (0, \frac{a^{2} e^{2} \tan θ}{b}) \end{array}$
equation of circle in which AB as diameter Passes through foci , then
$2 ae = 20 \Rightarrow e = 2 .$

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