ellipson

Topic:
Ellipse
In the diagram, a circle of radius $OA=2$ rolls around the inside of a circle of radius $OB=4$ with the half radius $AP=1$ originally positioned so that $P$ is on $OB$. Find a parameterization for the path that $P$ traces out as the inner circle rolls (without slipping.) Start by choosing an appropriate parameter. Is that a familiar curve?