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From the focus - 5 ,   0 of the ellipse x 2 45 + y 2 20 = 1 , a ray of light is sent which makes an angle cos - 1 - 1 5 with the positive direction of x -axis, upon reaching the ellipse surface, the ray is reflected from it. Slope of the reflected ray is

Options

  1. A- 3 2
  2. B- 7 3
  3. C- 5 4
  4. D- 2 11

Correct answer

D. - 2 11

Step-by-step solution

Ellipse: x 2 45 + y 2 20 = 1 Foci: ± 5 ,   0 Let's say θ = cos - 1 - 1 5 ⇒ cos θ = - 1 5   ⇒ tan θ = - 2 Now, equation of line passing through - 5 ,   0 and of slope - 2 can be written as y = - 2 x + 5 or y = - 2 x - 10 Now, if we solve this line with given ellipse equation x 2 45 + - 2 x - 10 2 20 = 1 This gives us point of intersection above x -axis at - 6 ,   2 . (Point - 3 , 4 will be rejected as slope of line joining it with focus will be 2 but slope of l

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