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

The vertices are on the x-axis at x = -5 and x = 5. The asymptotes have slopes of +3/5 and -3/5 and pass through the origin.

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, since the center is at the origin (0, 0), we have h = 0 and k = 0.

From the slope information we determine b = 3 and a = 5.

Hence the equation is , or

, or

.

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 either x=5 or -5, we get

, or , as we expect.

Now draw your graph, and then check it.