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

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