Equation of Cissoid of Diocles/Cartesian Form

Theorem
The cissoid of Diocles can be defined by the Cartesian equation:
 * $x \paren {x^2 + y^2} = 2 a y^2$

Also presented as
The Cartesian equation for the cissoid of Diocles can also be defined as:


 * $\dfrac {x^3} {2 a - x} = y^2$

which can be derived directly from the form given by subtracting $x y^2$ from both sides and dividing by $2 a - x$.

Also see

 * Equation of Cissoid of Diocles/Polar Form
 * Equation of Cissoid of Diocles/Parametric Form