Write the equation of and graph each conic described below.

1. A hyperbola that has foci at $\left(8, 5\right)$ and $\left(−12, 5\right)$ and the length of the transverse axis is $16$.

   Hint (a):

   From your sketch you should have determined that the hyperbola opens horizontally, $c = 10$, and $a = 8$.

2. An ellipse that has foci at $\left(−5, 12\right)$ and $\left(−5, −12\right)$ and the length of the minor axis is $10$.

   Hint (b):

   From your sketch you should have determined that the major axis of the ellipse is vertical, $c = 12$, and $b = 5$.