1. A circle C1 of radius 1 rolls counterclockwise along the outside of a circle C2 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 and intersect at right angles.
The wiki page does a pretty good job of explaining how they got the equation (see "Proof"). Do you see why the center of the small circle is ? And do you see that ? From there, it's just a matter of figuring out the coordinates of p.