Hello, New to this forum. First post. I thought I'd find the answer to this by Googling, but haven't! Anyway, the problem is to find the ellipse through 4 given points (or two points and the tangents at those points) that is the roundest, that is |a - b| is a minimum, where a and b are the major and minor axis. We can assume each given point lies outside the triangle formed by the other 3, not sure if that's any real help, but I believe it's necessary for an ellipse through the 4 points to exist (I think it might be sufficient, but have no proof as yet). Any ideas, or a solution, or have I missed it in your geometry section (I did take a quick look)? Thanks, Louis.