circle inversion

The inverse curve of the circle with parametric equations x | = | a cos t y | = | a sin t with respect to an inversion circle with center (x, y) and radius R is given by x_i | = | x_0 + (R(a cos t - x_0))/((x_0 - a cos t)^2 + (y_0 - a sin t)^2) y_i | = | y_0 + (R(a sin t - y_0))/((x_0 - a cos t)^2 + (y_0 - a sin t)^2), which is another circle.

circle | inversion