3 points is not enough information to completely determine an ellipse.
For example, you can always find a circle through 3 noncollinear points.
I see your point - the only condition I have is that the line of the major axis must pass through the center of the xy axis (0,0)(not the center of the ellipse). What about with four points? Is it too complicated? What I really want to know are the coordinates of the center of the ellipse.
That's it. And the problem is general, to be inserted in a C/C++ program. I have two choices:
1) The one I've explained
2) Or I could use an aprox. eccentrity - but I rather not use this choice because it would place the problem in 3D and the eccentrity is aprox. only.
If you cannot give a straight answer I will be closing this thread because all I have seen so far are people wasting time giving answers to questions that keep getting changed.
Ok. My answers are an aproximation to a problem. This is an astronomy problem.
I can generate the geocentric positions of the moon regarding the ecliptic (xy plane). What I need to know is the angle between the equinox (y=0) and the perigee. The ideal would be to construct the equation of an ellipse in 3D given the n points needed and then calculate the osculating elements (which I don't know how to do). The problem is that the osculating elements change from point to point, and the more points I use, the less precise I'll be.
What I was thinking is, since I want to calculate the perigee, was to project the 3 points into the xy axis ( it would be an ellipse too but I would have to disregard the eccentricity, which is aprox. too) and assume the barycenter (focus) as the Earth (0,0) - wich isn't accurate. But maybe I could get a certain precision. With the 4 points, I would need only the coordinates of the center or one of the focus to obtain the longitude of the perigee - but I loose precision by adding one extra point.
It's a little confusing...