I have attached the question.

I have managed to derive that;I only need help in the last part of the question.

$\displaystyle f(rcos(\theta),rsin(\theta))=\frac{(rcos(\theta))^ 3(rsin(\theta))}{r^6cos^6(\theta)+r^2sin^2(\theta) }=\frac{r^2cos^3(\theta)sin(\theta)}{r^4cos^6( \theta)+sin^2(\theta)}$

However I'm not sure about what this tells me about the plot of the graph nor am I sure of what to do next.