Question

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)`

Answer 1

Correct Answer - 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)`