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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?

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It looks very ill-posed to me... – J. M. Aug 3 '11 at 5:30
1. I would try to write the hyperbola in terms of lesser variables such that your constraint would be automatically satisfied, and then do the fit. 2. If you want to use the general method, you could enforce the constraint by applying it to input data -- symetrize your dataset along the symmetry axis you want to get, then the fit will be also symmetric. – eudoxos Aug 5 '11 at 13:28

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