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The line $ax + by + c = 0$ , meets the hyperbola $4 x^{2} - y^{2} = 4 p^{2}$ at P and Q. The point of intersection of the tangents at P and Q is

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$(\frac{p^{2} a}{c}, \frac{4 p^{2} b}{c})$

$(\frac{- p^{2} a}{c}, \frac{4 p^{2} b}{c})$

$(\frac{- p^{2} a}{c}, \frac{- 4 p^{2} b}{c})$

$(\frac{p^{2} a}{c}, \frac{- 4 p^{2} b}{c})$

answer is B.

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Detailed Solution

Hyperbola $\frac{x^{2}}{p^{2}} - \frac{y^{2}}{4 p^{2}} = 1$ ;

point of intersection of tangents = $(- \frac{a^{2} l}{n}, \frac{b^{2} m}{n}) = (\frac{- p^{2} a}{c}, \frac{4 p^{2} b}{c})$

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