Maltese Cross

Sketch the graph of $xy(x^2 - y^2) = x^2 + y^2$ consisting of four curves and a single point at the origin. Convert to polar form. Describe the symmetries of the graph.

Polar Bearings

What on earth are polar coordinates, and why would you want to use them?

Polar Flower

Age 16 to 18 Challenge Level:

Factorise the equation $$r^2 - r + {\textstyle{1\over 4}} \sin^2 4\theta = 0$$ and hence plot the graph given by this polar equation.