009C Sample Final 3, Problem 9

A wheel of radius 1 rolls along a straight line, say the  $x$-axis. A point  $P$  is located halfway between the center of the wheel and the rim; assume  $P$  starts at the point  ${\bigg (}0,{\frac {1}{2}}{\bigg )}.$  As the wheel rolls,  $P$  traces a curve. Find parametric equations for the curve.

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