Answer
$\frac{x^2}{4}-\frac{y^2}{5}=1$
See graph.
Work Step by Step
1. Given center $(0,0)$, focus $(-3,0)$, vertex $(2,0)$, we have a horizontal transverse axis, $c=3,a=2$ and $b=\sqrt {c^2-a^2}=\sqrt {9-4}=\sqrt 5$,
2. thus the equation is $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ or $\frac{x^2}{4}-\frac{y^2}{5}=1$
3. See graph.
