Answer
$\frac{(x+1)^2}{4}-\frac{(y-5)^2}{5}=1$
Work Step by Step
Step 1. From the given conditions, we have
$c=\frac{2+4}{2}=3, a=\frac{1+3}{2}=2$, thus $b^2=3^2-2^2=5$
Step 2. The center is at $(\frac{2-4}{2},5)$ or $(-1,5)$; thus we can write the equation as $\frac{(x+1)^2}{4}-\frac{(y-5)^2}{5}=1$
