Answer
$\frac{x^2}{9}-\frac{4y^2}{9}=1$ or $x^2-4y^2=9$; right branch.
Work Step by Step
Step 1. Use the figure given and rewrite the equation as $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. We have $a=3$ and $\frac{b}{a}=\frac{1}{2}$ (slope of the asymptote) with center at $(0,0)$ and a horizontal transverse axis.
Step 2. Thus, we have $b=\frac{3}{2}$ and the equation becomes $\frac{x^2}{9}-\frac{4y^2}{9}=1$ or $x^2-4y^2=9$ (right branch).
