Question

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

Answer 1

These parametric equations represent a circle x² + y² = r² with centre at origin, say O, and radius r.

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