Answer
$\frac{x^2}{4}-\frac{y^2}{24}=1$
Work Step by Step
Vertices: $(±a,0)=(±2,0)$
$a=2$
Hyperbola with horizontal transverse axis:
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
$\frac{x^2}{2^2}-\frac{y^2}{b^2}=1$
$\frac{x^2}{4}-\frac{y^2}{b^2}=1$
The hyperbola passes through the point $(3,\sqrt {30})$:
$\frac{3^2}{4}-\frac{(\sqrt {30})^2}{b^2}=1$
$\frac{9}{4}-\frac{30}{b^2}=1$
$\frac{9}{4}-1=\frac{30}{b^2}$
$\frac{5}{4}=\frac{30}{b^2}$
$b^2-24$
Finally:
$\frac{x^2}{4}-\frac{y^2}{24}=1$
