The Inverse of a Parabola

Given is a parabola, defined by its focus point and . We perform inversion with respect to the circle with center and radius r. Point D is a point on the circle. We can change the radius by dragging . Point is a random point on the parabola. Point is the image of under inversion with respect to the above circle (). As moves along the parabola, will draw the locus of the inverse of the parabola. If the center of the circle is in the focus of the parabola, the inverse of the parabola is a Limaçon with a cusp (a Cardioid). [list]