Answer
It is a hyperbola.
See Graph I for the graphing of the equation.
Work Step by Step
For $9x^2 - 4y^2 = 36$, it can be rewritten as
$\frac{9x^2}{36} - \frac{4y^2}{36} = \frac{36}{36}$
$\frac{x^2}{4} - \frac{y^2}{9} = 1$
$\frac{x^2}{2^2} - \frac{y^2}{3^2} = 1.$
It is in the form of a hyperbola.
The $x-intercepts$ are at $\pm2$.
See Graph I for the graphing of the equation.