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

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Solution

The correct option is C
10

$\frac{2 a}{e} = 4 \Rightarrow$ a = 2e, P is nearest to 3x + 4y - 10 = 0

$\Rightarrow a e - \frac{a}{e} = 8 \Rightarrow e = \sqrt{5}, a = 2 \sqrt{5}$

CP = ae = 10

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