I've been doing some digging, and according to several sources 5 points in a plane determine a unique conic - 4 points allows you an infinite family called a pencil of conics (see this link ellipse from 4 points).
So, I've found a C program (http://mathforum.org/library/drmath/view/51735.html) that does that - but I'm changing it. From there, I'll get the general equation (if sucessful) of the ellipse. The problem will be to find the values of the center, semi-axis, etc. Not to speak in the lost of precision since I've be using a set of five points.