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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

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 $\theta$.