The locus of the point of intersection of the tangents to the circle x=rcosθ, y=rsinθ at points whose parametric angles differ by π3 is

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x2+y2=4(2−3)r2

3(x2+y2)=r2

(x2+y2)=(2−3)r2

3(x2+y2)=4r2

answer is D.

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Detailed Solution

let the angles be 0 and π3Tangents at θ=0 and θ=π3 are x=r and xcos(π3)+ysin(π3)=r ⇒x=r, y=r3⇒ 3(x2+y2)=4r2

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