Find hyperbola (with oblique axes) given asymptotes

What is the general equation for a hyperbola with asymptotes y = m1x+c1, y = m2x+c2, where point(s) on the hyperbola are known, and the hyperbola may be oblique (i.e. not horizontal or vertical facing)?

My particular problem is that I have the graph of the curve (from data) and therefore can determine asymptotes, centre, intercepts etc, but want to find the equation of the hyperbola from these.

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Re: Find hyperbola (with oblique axes) given asymptotes

Hi !

Knowing a lot of points of the hyperbola curve, you can permorm a regression (least squares fitting) in order to obtain the coefficients of the quadratic equation of the hyperbola.

A less accurate method consists in performing first a graphical approximation of the equations of the asymptotes. Then, the approximate quadratic equation of the hyperbola can be derived (see attachment)

For more information about quadratic curve fitting, the paper "Regressions coniques, quadriques, circulaire, sphérique..." (in French, not translated yet)

through the link : Scribd

Re: Find hyperbola (with oblique axes) given asymptotes

That's great, thanks very much!