Hyperbola: Equation from a graph: Simple: Determine the equation of the hyperbola in this graph:

We need to determine the general equation in the form , with asymptotes of slopes +b/a and -b/a. (h, k) are the coordinates of the center of the hyperbola.

In this case, the center is at the origin, so h = 0 and k = 0.

The distance from the center to a vertex is the value of "a". Here that is 5, so a = 5.

The slopes of the asymptotes are +b/a and -b/a. Here the slope is 3/5, so that b = 3.

Substituting in the general equation, we get

, or