My goal is to find the equation of an ellipsis to fit the following points:
(0.120727960995591, 1.40351716270739)
(0.556408255451578, 1.22358316257310)
(0.986940854500628, 0.782393903020727)
(1.12685887538981, -0.00110809554252468)
(0.949400714131023, -0.421663826229138)
(0.618511570455713, -0.738619832947234)
Given the general formula for the curve is $$Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$$
in this link I created the matrix with the coefficients $x^2$, $xy$, $y^2$ and so on, as to find its inverse and, after that, the solution to the problem. Given that matrix B is a null matrix, the only solution that I get is the trivial one.
So my question is: is it really possible to find the equation of the ellipsis in such a way? Or is it necessary to use a numerical method?
Thanks in advance.