Answer
$\displaystyle \frac{x^{2}}{13}+\frac{y^{2}}{9}=1$
Work Step by Step
With the given information,
the foci are $c=2$ units left/right of the point (0,0)
so, the major axis is horizontal,
so, the standard form the equation is
$\displaystyle \frac{(x-h)^{2}}{a^{2}}+ \displaystyle \frac{(y-k)^{2}}{b^{2}}=1$.
The y-intercepts give: $b=3$.
$(h,k)=(0,0)$
$b=3$
$c=2$
From $c^{2}=a^{2}-b^{2}$
$a^{2}=b^{2}+c^{2}=9+4=13$
so the equation is
$\displaystyle \frac{x^{2}}{13}+\frac{y^{2}}{9}=1$
