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Question

A ray originating from the point (5, 0) is incident on the hyperbola 9x2 16y2 = 144 at the point P with abscissa 8. Find the equation of the reflected ray after first reflection and point P lying in first quadrant.


A

33x 13y + 153 = 0

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B

33x 13y 153 = 0

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C

33x + 13y + 153 = 0

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D

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Solution

The correct option is A

33x 13y + 153 = 0


Given hyperbola is 9x2 16y2 = 144.

This equation can be rewritten as

x216 y29 = 1 - - - - - - (1)

Since x co-ordidate of p is 8.

Let y co-ordinate of p is α.

(8 , α) lies on hyperbola x216 y29 = 1

6416 a29 = 1

α2 = 27

α = 33 (p lies in first quadrant)

Hence co-ordinate of point p is (8 , 33).

Equation of reflected ray passes through

p(8 , 33) and other focus s'(-5,0)

its equation is y 33 = 03358 (x 8)

or 13y 393 = 33x 243

or 33x 13y + 153 = 0


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