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