Problem source

The curve $C$ has the equation $x^3+y^3 = 3xy$.
\begin{questionparts}
\item Show that there is no point of inflection on $C$. You may assume that
the origin is not a point of inflection.
\item The part of $C$ which lies in the first quadrant is a closed loop
touching the axes at the origin. By converting to polar coordinates,
or otherwise, evaluate the area of this loop. 
\end{questionparts}