# The locus of the point of intersection of the tangents to the circle x=r cosy , y=r siny at the points whose parametric angles differ by pi/s is a)x2+y2=r2 b)x2+y2=2r2 c)3(x2+y2)=2r2 d)3(x2+y2)=4r2

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by sharmi

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by sharmi

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Take two points A and B on the circumference of the circle such that angle AOB = 90 (i.e.,π/2). Let tangents at A and B meet at point P(X,Y).

Distance OP of point P from centre O is given by OP² = X² + Y² -------(1)

AOBP is a square with side r.

Therefore OP is a diagonal of square AOBP of side r,

hence OP² = 2r² --------(2)

From (1) and (2), X² + Y² = 2r²

Hence using general co-ordinates.locus of point is given by x² + y² = 2r²