Haff Ellipsograph
The coordinates of the centers of the two circles are:
(0, -p sin(α))
(p cos(α), 0)
The purple point on on the line joining the centers with coordinates (p cos(α), 0) + k p (cos(α), sin(α)) = ((k+1) p cos(α), k p sin(α)) so must lie on the ellipse
(x/(k+1))^2 + (y/k)^2 = p^2
