Thanks, I'll note that. Still, I am looking for the best approximation into the elliptic arc. For example, in this paper, the method for the inverse problem is described. The error of approximation of elliptic arc to bezier curve is negligible. I am looking for the same kind of method, but inverse to the one described in that paper.

0≤𝑡≤1 corresponds to the limits of $x$ and $y$ for the elliptic arc, so this puts the limits onto $x$ and $y$ that can be supplied into the ellipse equation 𝑄(𝑥,𝑦)=0. Are you stating that even within those limited ranges x(0)≤x≤x(1) and y(0)≤y≤y(1) for the ellipse equation 𝑄(𝑥,𝑦)=0 they are still not identical?