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:
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:
Asymptotes (in magenta color) and vertices.
Completing the hyperbola:
"East-West" hyperbola (in green) with its asymptotes (in magenta color).
Easy to understand math videos: