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Question

The normal at P(θ) and D(θ+π2) meet the major axis of x2a2+y2b2=1 at Q and R. Then PQ2+DR2=

A
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B
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C
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D
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Solution

The correct option is B
Equation of the normal at P(θ) is axcosθbysinθ=a2e2
This normal meets the major axis at Q = (ae2cosθ,0)
Equation of the normal at D(π2+θ) ie D(asinθ,bcosθ) is axsinθbycosθ=a2e2
This normal meets the major axis at R =(ae2sinθ,0)
PQ2+DR2=[(ae2cosθacosθ)2+b2sin2θ]+[(ae2sinθasinθ)2+b2cos2θ]
=a2(1e2)(2e2) [on simplification]

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