Answer
The equation matches with the graph labeled as I.
Work Step by Step
$9x^2-25y^2=225$
$\frac{x^2}{25}-\frac{y^2}{9}=1$
Hyperbola with a horizontal transverse axis:
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
$a^2=25$
$a=5$
Vertices: $(±a,0)=(±5,0)$
The hyperbole with vertices in $(±5,0)$ is the graph labeled as I.
