Answer
$-\frac{x^2}{51}+\frac{y^2}{49}=1$
Work Step by Step
Step 1. With the given conditions, we have
$c=\frac{10+10}{2}=10, a=\frac{7+7}{2}=7, b=\sqrt {10^2-7^2}=\sqrt {51}$
and the foci are on the y-axis.
Step 2. The center is at $(0,0)$; thus we can write the equation as $-\frac{x^2}{51}+\frac{y^2}{49}=1$
