Chapter 10.4, Problem 22ES

Find an equation for the ellipse that satisfies the given conditions.

$\begin{array}{l}\left(\text{a}\right)\text{Center}\text{at}\left(0,0\right);\text{major and minor axes along the}\text{coordinate}\text{axes; passes through}\left(3,2\right)\text{and}\left(1,6\right).\\ \left(\text{b}\right)\text{Foci}\left(2,1\right)\text{and}\left(2,-3\right);\text{major axis of length 6}\text{.}\end{array}$