The graph of xy=0 is the pair of lines x=0 and y=0. Similarly
you will need to draw a pair of graphs here but this time in polar
coordinates.
When you plot the point (r,\theta) in polar coordinates, the
length of the line segment joining this point to the origin is r
and the angle between this line segment and the positive direction
of the x axis is given by \theta.
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.