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Consider a hyperbola: ((x-7)^(2))/(a^2) ...

Consider a hyperbola: `((x-7)^(2))/(a^2) -((y+3)^(2))/(b^(2)) =1`. The line `3x - 2y - 25 =0`, which is not a tangent, intersect the hyperbola at `H ((11)/(3),-7)` only. A variable point `P(alpha +7, alpha^(2)-4) AA alpha in R` exists in the plane of the given hyperbola.
The eccentricity of the hyperbola is

A

`sqrt((7)/(5))`

B

`sqrt(2)`

C

`(sqrt(13))/(2)`

D

`(3)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
The given line must be parallel to asymptotes
`rArr` Slope of asymptotes are `(3)/(2)` and `-(3)/(2)`
`rArr (b)/(a) =(3)/(2) rArr e = (sqrt(13))/(2)`
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