Let P(x, y) be a variable point such that
`|sqrt((x-1)^(2)+(y-2)^(2))-sqrt((x-5)^(2)+(y-5)^(2))|=3`
which represents a hyperbola.
IF the origin is shifted to the point (3, 7/2) and the axes are rotated through an angle `theta` in clockwise sense so that the equation of the given hyperbola changes to the standard form `(X^(2))/(a^(2))-(y^(2))/(b^(2))=1`, then `theta` is

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)`