Answer
$\displaystyle \frac{(x-2)^{2}}{25}+ \displaystyle \frac{(y+3)^{2}}{100}=1$
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 $2b$
$2a=20 \Rightarrow a=10$
$2b=10\Rightarrow b=5$
Center: $(h,k)=(2,-3)$
$\displaystyle \frac{(x-2)^{2}}{5^{2}}+ \displaystyle \frac{(y-(-3))^{2}}{10^{2}}=1$
$\displaystyle \frac{(x-2)^{2}}{25}+ \displaystyle \frac{(y+3)^{2}}{100}=1$
