Given a set of points $(x_i, y_i)$ in $\mathbb{R}^2$, I can find the best fit hyperbola in the least squares sense by using the method given here.
But, is there a way to constrict the hyperbola to have a specific point lie on its axis of symmetry? That is, if I have an additional point $(x^*,y^*)$ that I know lies on the axis of symmetry (line connecting the foci) but not necessarily on the hyperbola itself, is there a method to find the constrained best fit hyperbola?