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