An ellipse has a center at the origin, a vertex along the major axis at (0, 17), and a focus at (0, −8). which equation represents this ellipse?

We know that
Since the focus and vertex are above and below each other, rather than side by side, I know that this ellipse must be taller than it is wide.
Then 
a² will go with the y part of the equation
Also, since the focus is 8 units below the center, then c = 8
since the vertex is 17 units above, then a = 17
The equation b² = a² – c² gives me
b²=17²-8²-----> b²=225
the equation is
y²/a²+x²/b²=1------> y²/289+x²/225=1

the answer is
y²/289+x²/225=1

see the attached figure

Uneed to add them up 27+18+23=68