# The Inverse of a Parabola

- Author:
- Irina Boyadzhiev

- Topic:
- 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]