Home
Class 12
MATHS
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

A. `-(3)/(2)`

B

B. `-(7)/(3)`

C

C. `-(5)/(4)`

D

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)`
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|6 Videos

  • DOT PRODUCT

    CENGAGE PUBLICATION|Exercise DPP 2.1|15 Videos

  • EQAUTION OF STRAIGHT LINE AND ITS APPLICATION

    CENGAGE PUBLICATION|Exercise DPP 3.2|13 Videos

Similar Questions

Explore conceptually related problems

The eccentricity of the ellipse 5x^(2) + 9y^(2) = 1 is _

A ray of light is sent along the lie x-2y+5=0, upon reaching the line 3x-2y+7=0, the ray is reflected from it. Then the equation of the line containing the reflected ray is-

A ray of light is sent along the line x-2y-3=0 upon reaching the line 3x-2y-5=0, the ray is reflected from it .Find the equation of the line containing the reflected ray.

A ray of light is sent along the line x-2y-3=0 upon reaching the line 3x-2y-5=0, the ray is reflected from it. Find the equation of the line containing the reflected ray.

A ray light along x+sqrt3y = sqrt3 gets reflected upon reaching the x-axis, the equation of the reflected ray is

Let the equation of an ellipse be (x^(2))/(144) + (y^(2))/(25) = 1 . Then the radius of the circle with centre (0 , sqrt(2)) and passing through the foci of the ellipse is _

A ray of light is sent along the line x-2y+5=0 , upon reaching the line 3x-2y+7=0 , the ray is reflected from it Find the equation of the line containing the reflected ray.

A ray of light along x+sqrt(3)y=sqrt(3) gets reflected upon reaching x-axis , the equation of the reflected ray is

Find the eccentric angle of a point on the ellipse (x^2)/6+(y^2)/2=1 whose distance from the center of the ellipse is sqrt(5)

Find the angle which a line perpendicular to the line x-y+1=0 makes with the positive direction of the x axis.