Let `P(x, y)` is a variable point such that `|sqrt((x-1)^2+(y-2)^2)-sqrt((x-5)^2+(y-5)^2)|=3` , which represents hyperbola. The eccentricity e' of the corresponding conjugate hyperbola is (A) `5/3` (B) `4/3` (C) `5/4` (D) `3/sqrt7`

Options

A. `5//3`
B. `4//3`
C. `5//4`
D. `3//sqrt7`

Answer

C

Explanation

2a = 3
Distance between the foci (1, 2) and (5, 5) is 5. Therefore,
2ae = 5
`"or "e=(5)/(3)`
Now, if e' eccentricity of the corresponding conjugate hyperbola, then
`(1)/(e^(2))+(1)/(e'^(2))=1`
`"or "e'=(5)/(4)`