Hyperbola: Equation from a graph: 1st Quadrant: Find the standard 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.

Here the center is at (2, 3), so we have h = 2 and k = 3. Since "a" is the distance from the center to a vertex, we see that the distance is 4, and a = 4. From the diagram we see that the slopes of the asymptotes are 2/4 and -2/4. Hence b = 2. Combining these results, we get