Answer
$\displaystyle \frac{(x+2)^{2}}{4}+ \displaystyle \frac{(y-3)^{2}}{25}=1$
Work Step by Step
Major axis vertical: $\displaystyle \frac{(x-h)^{2}}{b^{2}}+ \displaystyle \frac{(y-k)^{2}}{a^{2}}=1$
Major and minor axes have lengths $2a$ and $2b$
$2a=10 \Rightarrow a=5$
$2b=4\Rightarrow b=2$
Center: $(h,k)=(-2,3)$
$\displaystyle \frac{(x-(-2))^{2}}{2^{2}}+ \displaystyle \frac{(y-3)^{2}}{5^{2}}=1$
$\displaystyle \frac{(x+2)^{2}}{4}+ \displaystyle \frac{(y-3)^{2}}{25}=1$
