A curve $D$ has parametric equations $x=k\left( 2\cos heta -\cos 2 heta ight)$ $y=-k\sin 2 het

Question

A curve $D$ has parametric equations $x=k\left( 2\cos 	heta -\cos 2	heta ight)$ $y=-k\sin 2	heta $ for $0Find, in terms of $k$, the exact coordinates of the stationary points of $D$. [3] Sketch the graph of $D$, labelling, in terms of $k$, the points where $D$ meets the $x$-axis. [2]

Accepted Answer

Stationary points: $(\sqrt{2}k, -k)$ and $(-\sqrt{2}k, k)$

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