A circle C of radius 2r has its center at the origin. A circle
of radius r rolls without slipping in
the counterclockwise direction around C. A point P is located on a
fixed radius of the rolling
circle at a distance b from its center, 0 < b < r as
shown:
Graph (ii) shows the case when b = r. Let L be the line from the
center of C to the center of
the rolling circle and let be the angle that L makes with the
positive x-axis.
Using as a parameter, find parametric equations
of the path traced out by P.