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A hyperbola has centre 'C" and one focus...

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

A

14

B

8

C

10

D

6

Text Solution

Verified by Experts

The correct Answer is:
C
Distance between directrixes `= (2a)/(e) =4`.
`rArr a = 2e`.
P is nearest to `3x + 4y - 10 =0`
Distance of P from this directrix is
`rArr ae - (a)/(e) =8`
`rArr e = sqrt(5), a=2 sqrt(5)`
`rArr CP = ae = 10`
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