Answer
$\displaystyle \frac{x^{2}}{9}-\frac{y^{2}}{4}=1$
Work Step by Step
The branches of the graph indicate that
the transverse axis is horizontal,
the center is at the origin,
the form of the equation is $\displaystyle \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$.
From the graph,
$a=3,$
$b=2$
$\displaystyle \frac{x^{2}}{9}-\frac{y^{2}}{4}=1$
