Answer
$x^2-\frac{y^2}{8}=1$
See graph.
Work Step by Step
1. Given center $(0,0)$, focus $(3,0)$, vertex $(1,0)$, we have a horizontal transverse axis, $c=3,a=1$ and $b=\sqrt {c^2-a^2}=\sqrt {9-1}=2\sqrt 2$,
2. thus the equation is $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ or $x^2-\frac{y^2}{8}=1$
3. See graph.
