Answer
$\displaystyle \frac{(x-7)^{2}}{4}+\frac{(y-6)^{2}}{9}=1$
Work Step by Step
Endpoints of major axis are above/below each other, so
the major axis is vertical, so
$\displaystyle \frac{(x-h)^{2}}{b^{2}}+ \displaystyle \frac{(y-k)^{2}}{a^{2}}=1$
is the equation form.
The center is the midpoint of the vertices:
$(h,k)=(\displaystyle \frac{7+7}{2},\frac{9+3}{2})=(7,6)$
Major and minor axes have lengths $2a$ and $2b$
$2a=9-3=6 \Rightarrow a=3$
$2b=9-5=4\Rightarrow b=2$
$\displaystyle \frac{(x-7)^{2}}{4}+\frac{(y-6)^{2}}{9}=1$
