Hyperbola: Graph from description: 1st Quadrant: Find the standard equation and draw the graph for the hyperbola described as follows:

The vertices are at (-2, 3) and (6, 3). The asymptotes have slopes of +2/4 and -2/4 .

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 vertices have the same y-coordinate, and must lie on the line y = 3. The center (h, k) will be midway between, or at (2, 3). Hence, we have h = 2 and k = 3.

From the slope information we determine b = 2 and a = 4.

Hence the equation is .

We can check our results by substituting the x-coordinate of a vertex into the original equation and determining the corresponding y-coordinate. It should agree with the value of k, the y-coordinate of the center and the vertices. Using x = 6, we get

, or

, or

, or

, and the value of y agrees with the y-coordinate of the vertex, k = 3. You can check in a similar way with the x-coordinate of the other vertex: x = -2.

Now draw your graph, and then check it.