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Question

If co-ordinates of P and Q are (acosθ,bsinθ) and (asinθ,bcosθ) respectively , then show that OP2+OQ2=a2+b2, where O is origin.

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Solution

P=(acosθ,bsinθ) Q=(asinθ,bcosθ)

0 is the origin

OP2+OQ2=[(0acosθ)2+(0bsinθ)2]2+[(0+acosθ)2+(0bsinθ)2]2

=a2cos2θ+b2sin2θ+a2sin2θ+b2cos2θ

=a2[cos2θ+sin2θ]+b2[cos2θ+sin2θ]

=a2+b2

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