${\displaystyle x^{3}+y^{3}-3axy=0\quad {\text{for}}\quad a=1}$

Polar coordinates:

${\displaystyle r=3a{\frac {\sin \varphi \cos \varphi }{\sin ^{3}\varphi +\cos ^{3}\varphi }}}$

Cartesian coordinates:

${\displaystyle (x,y)=3a{\Bigl (}{\frac {t}{1+t^{3}}},{\frac {t^{2}}{1+t^{3}}}{\Bigr )}}$

To draw, I used the following parametrization:

${\displaystyle (x,y)=(-(1+t)u,tu)\quad {\text{with}}\quad u=v/(1+v),\;v=3t(1+t)}$