An example of a prolate cycloid, with $a=2$ and $b=4,$ is shown in Figure $1.34.
(When $a Using vector methods or otherwise, find a set of parametric equations for the curtate cycloid. One such cycloid appears in Figure $1.32,$ where $a=3$ and $b=2$. If a reflector is attached to a spoke of the wheel at a distance $b$ from the center, the resulting curve traced by the reflector is called a curtate cycloid. Suppose that a bicycle wheel of radius $a$ rolls along a flat surface without slipping.
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