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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 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 $\theta$.