What do you get when you inverse a circle?

Geometry Level pending

O is a fixed point. Consider a given circle. Let P be any point on this circle. OP is joined and on it a point Q is taken so that OP.OQ= a constant quantity k^2 ; find the locus of Q when
(i) O does not lie on the original circle
(ii) O lies on the original circle?

The fixed point is called centre of inversion and when a curve is obtained from the first curve by this geometrical method, it is called the inverse of the first curve.

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