If a ray of light incident along the line `3x+(5-4sqrt(2))y=15` gets reflected from the hyperbola `(x^2)/(16)-(y^2)/9=1` , then its reflected ray goes along the line. `xsqrt(2)-y+5=0` (b) `sqrt(2)y-x+5=0` `sqrt(2)y-x-5=0` (d) none of these

Options

A. `xsqrt2-y+5=0`
B. `sqrt2y-x+5=0`
C. `sqrt2y-x-5=0`
D. none of these

Answer

D

Explanation

The given hyperbola is
`(x^(2))/(16)-(y^(2))/(9)=1`
`therefore" "e=(5)/(4)`
Its foci are `(pm5,0)`.

The ray is incident at `P(4sqrt2,3)`.
The incident ray passes through (5, 0), so, the reflected ray must pass through `(-5,0)`.
Its equation is
`(y-0)/(x+5)=(3)/(4sqrt2+5)`
`"or "3x-y(4sqrt2+5)+15=0`