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. As the wheel rolls, $P$ traces a curve. Find parametric equations for the curve.

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

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