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Q.

If P(3secθ ,2tanθ) and Q(3secϕ ,2tan ϕ) where θ+ϕ=π2, be two distinct points on the hyperbola x29-y24=1. Then the ordinate of the points of intersection of the normals at P and Q is 

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a

-113

b

-132

c

113

d

132

answer is D.

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Detailed Solution

Given hyperbola x29-y24=1

a2=9, b2=4

Equation of normal at P(3secθ, 2tanθ) is

3xsecθ+2ytanθ=13 3x cosθ+2y cotθ=13 (1) Equation of normal at 0 (3se, 2tan) is 3x cos+2y cot=13 3x sinθ+2y tanθ=13 (2)  (=π2-θ) (1)×sinθ-(2)×cosθ 2y(cosθ-sinθ)=13(sinθ-cosθ) 2y=-13 y=-132.

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