A hyperbola has centre C and one focus at P(6, 8). If its two directrices are $3 x + 4 y + 10 = 0$ and $3 x + 4 y - 10 = 0$ then CP =

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Solution

The correct option is C 10
$\frac{2 a}{e} = 4 \Rightarrow a = 2 e$ , P is nearest to $3 x + 4 y - 10 = 0$
$\Rightarrow a e - \frac{a}{e} = 8 \Rightarrow e = \sqrt{5}, a = 2 \sqrt{5}$
CP = ae = 10

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