Question

How would I find the equation of an ellipse with center (4,3), vertex (4,-3) and a focus of (4,2)?

Answer 1

I know the top part would be:
(y-3)^2/... + (x-4)^2/... =1, but I don't know what is on the bottom.

Answer 2

\[ c=1\\
b=6\\
b^2 = a^2 -c^2\\
36 = a^2 -1\\
a^2 = 37\\
\frac {(x-4)^2}{37} +\frac {(y-3)^2}{36}=1

\]