Cissoid of Diocles - Inversion

Inversion

The cissoid of Diocles also be defined as the inverse curve of a parabola with the center of inversion at the vertex. To see this, take the parabola to be x=y2. In polar coordinates this becomes

,

and the inverse curve then has equation

which is a special case of the equation defining the cissoid of Diocles on polar coordinates.