Folium of Descartes

In geometry, the folium of Descartes (from Latin folium 'leaf'; named for René Descartes) is an algebraic curve defined by the implicit equation

${\displaystyle x^{3}+y^{3}-3a\cdot xy=0.}$

${\displaystyle dy/dx=(x^{2}-ay)/(ax-y^{2}),\,dx/dy=(ax-y^{2})/(x^{2}-ay).}$