Oh, I forgot to answer that question:

No, I am not at all interested in any graphics stuff! I just want the parameters for the ellipses. 5 numbers for each one of them.

I just drew those figures now in order to help explain the mathematical problem. That red-green-blue thing maybe was confusing. I did it just to explain that for each of the ellipse halves (the colored ones) there belongs a certain set of points. The points and ellipses and circles actually have no colors. They are just mathematical abstractions. The points are randomly distributed around each of their ellipse (half).
This part I don't understand. But it doesn't sound like anything I am interested in!

Please, before you put any work into this, please clear things out with me. It is so easy to misunderstand, especially since I am not used to strict mathematical language.

I want to put in 2D coordinates for two or three sets of points, together with radii and distances defining the circles' relations to each other, and get back the ellipse parameters that fits it best according to least square or something like that.

I guess one makes an initial guess for parameters of one of the ellipses, then uses the geometry of the circles to calculate which parameter this implies for the other ellispes. Then one calculates the fit (least square or something like that). Then iterates and refits until the fit is good enough. From the geometry of it, one needs to formulate some optimization function which hopefully can have its derivatives solved so that an efficient numerical method can be applied.

There is a duality between the 2D projection, where there exists ellipses and points; and the 3D physical world, where there exists circles. A certain angle in the 3D world, corresponds to the length of an ellipse axis in the 2D projection.