The locus of the point of intersection of tangents to the circle x=acosθ,y=asinθ at the points, whose parametric angles differ by π2 is
A
a straight line
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B
a circle
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C
a pair of straight lines
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D
None of these
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Solution
The correct option is B a circle x=acosθ,y=asinθ ⇒S:x2+y2=a2 Let from point P, tangents are drawn. ∵∠AOB=π2, ∴∠APB=π2 So, tangents are perpendicular to each other. Hence P will lie on director circle of S which is also a circle.