The locus of the point of intersection of tangents to the circle x=a cos θ, y=a sin θ at the points, whose parametric angles differe by (π)/2 , is

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Correct answer: (B) a circle. We have, the given circle x=a cos θ, y=a sin θ ⇒ x^2+y^2=a^2...(i) Tangents to the circle (i) at θ and (θ+(π)/2 ) are x cos θ+y sin θ=a and x cos (θ+(π)/2 )+y sin (θ+(π)/2 )=a or x cos θ+y sin θ=a and -x sin θ+y cos θ=a Squaring and adding, we get x^2+y^2=2 a^2 which is a circle.

The locus of the point of intersection of tangents to the circle $x=a \cos \theta, y=a \sin \theta$ at the points, whose parametric angles differe by $\frac{\pi}{2}$, is

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