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From the focus (-5,0) of the ellipse (x^...

From the focus `(-5,0)` of the ellipse `(x^(2))/(45)+(y^(2))/(20) =1`, a ray of light is sent which makes angle `cos^(-1)((-1)/(sqrt(5)))` with the positive direction of X-axis upon reacting the ellipse the ray is reflected from it. Slope of the reflected ray is

A

`-(3)/(2)`

B

`-(7)/(3)`

C

`-(5)/(4)`

D

`-(2)/(11)`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `theta = cos^(-1) ((-1)/(sqrt(5))) rArr cos theta = (-1)/(sqrt(5)) rArr tan theta =-2`
Foci are `(+- 5,0)`
Equation of line through `(-5,0)` with slope `-2` is `y =- 2(x+5)` or `y =- 2x -10`
This line meets the ellipse above X-axis at `(-6,2)`
Reflected ray passes through the other focus `(5,0)`
`:.` Slope `= (2-0)/(-6-5) =- (2)/(11)`
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