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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.

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Polar Bearings

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

Polar Flower

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The point $P$ with polar coordinates $(r,\theta)$ is such that $OP=r$ and the angle between the x-axis and the line through $OP$ is $\theta$ measured counter clockwise. Equivalently if $P$ has Cartesian coordinates $(x,y)$ then $x=r\cos \theta$ and $y=r\sin \theta$.

The question asks for an explanation of the features of the graph. If you want to use a software package to sketch the graph you may want to download the shareware graphing software Graphmatica .