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 3√3x − 13y + 15√3 = 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 = 3√3 (∵p lies in first quadrant) Hence co-ordinate of point p is (8 , 3√3). ∵ Equation of reflected ray passes through p(8 , 3√3) and other focus s'(-5,0) ∴ its equation is y − 3√3 = 0−3√3−5−8 (x − 8) or 13y − 39√3 = 3√3x − 24√3 or 3√3x − 13y + 15√3 = 0

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