A story I wrote depends on some geometry, and I want to get it straight. Assumptions: 1] The 2D math that applies to circles and ellipses is analagous to the 3D math for spheres and ellipsoids in the ways relevant to the rest of my post. 2] An ellipse is a circle whose two foci are co-incident. Thus, a sphere is an ellipsoid whose two foci are co-incient. What I want to figure out is what happens to the surface of an ellipse/ellipsoid when the two co-incident foci are moved apart. Say I have a sphere of unit radius. I move its two foci two units apart. What happens to the surface? What is the length of its semi-minor axis? What is the length of its semi-major axis? And, more specifically, what happens to the distance from focus-to-surface near the "ends"? Does the distance from focus to surface decrease as the ellipsoid "stretches" thinner? (i.e. is the focus now closer to the surface than one unit?) [ EDIT ] The correct term for my shape is a prolate spheroid - a cigar shape**. Equatorial radii a and b are the same. Polar radius c is longer. ** by magical coincidence, I am writing this while smoking a cigar.