Trident of Descartes

$\begin{figure}\begin{center}\BoxedEPSF{trident_descartes.epsf}\end{center}\end{figure}$

The plane curve given by the equation

$\begin{displaymath} (a+x)(a-x)(2a-x)=x^3-2ax^2-a^2x+2a^3 = axy \end{displaymath}$

$\begin{displaymath} y = {(a+x)(a-x)(2a-x)\over ax}. \end{displaymath}$

The above plot has