# Find hyperbola (with oblique axes) given asymptotes

• Sep 3rd 2012, 03:54 AM
stevenson2012
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.
• Sep 3rd 2012, 05:25 AM
JJacquelin
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)