This is an east-west opening hyperbola, with a = 3 and b = 4. It will look similar to the east-west opening Example 2, given above.

x-intercepts: Letting y = 0 in the equation given in the question, and we have:

Solving gives us:

x = -3 and x = 3

Aymptotes: We have an east-west opening hyperbola, so the slopes of the asymptotes will be given by

In this example, a = 3 and b = 4. So the slopes of the asymptotes will be simply:

-4/3 and 4/3.

The equations for the asymptotes, since they pass through (0, 0), are given by:

y = -4x/3 and y = 4x/3

Including the above information on our graph:

Completing the hyperbola: