fitlm for ellipse fitting

I have a matrix with x and y coordinates that resemble an ellipse. I would like to fit an ellipse through these coordinates using fitlm because of its robustness. I intend to use X = [x.^2, x.*y, y.^2, x, y] as the predictor variables but I don't know how to define the response variables. Can anyone help me with this? Is actually even possible to use both x and y as predictor variables in the form that I mentioned?