1. A circle C_{1}of radius 1 rolls counterclockwise along the outside of a circle C_{2}of radius 4 which is centered at the origin. Assume that there is a point P on the circumference of the circle C1 that sits intially at the point (4,0). Find a parametric curve describing the way that P traces in the plane.

My idea of whats going on: imgur: the simple image sharer

2. For a<0 show that the polar curves $\displaystyle r=asin(t)$ and $\displaystyle r=acos(t)$ intersect at right angles.