# Equation of Cissoid of Diocles

## Theorem

Let $C$ be a circle of radius $a$ whose circumference passes through the origin $O$ and whose diameter through $O$ lies on the horizontal.

### Polar Form

The cissoid of Diocles can be defined by the polar equation:

$r = 2 a \sin \theta \tan \theta$

### Cartesian Form

The cissoid of Diocles can be defined by the Cartesian equation:

$x \paren {x^2 + y^2} = 2 a y^2$

### Parametric Form

The cissoid of Diocles can be defined by the parametric equation:

$\begin {cases} x = 2 a \sin^2 \theta \\ y = \dfrac {2 a \sin^3 \theta} {\cos \theta} \end {cases}$