Operating with the selection-tool (CTRL+1), catch and move X along a curve. Y descrribes the inverse of X w.r. to an inversion with center at O:
(OX)*(OY) = a^2 - b^2 = r = constant.
When X travels along any arbitrary curve, Y describes a curve that is the inversion of the first one. O is the center of inversion r is the power of the inversion.