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.