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

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

`x^2/9=1`

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

`+-b/a`

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:

5-55-5xy−33Open image in a new page

Asymptotes (in magenta color) and vertices.

Completing the hyperbola:

5-55-5xyOpen image in a new page

"East-West" hyperbola (in green) with its asymptotes (in magenta color).

Easy to understand math videos:
MathTutorDVD.com