This foci/ellipse question...?

Question

Which of the following will have a focus at (–2, 0) and a vertex at (5, 0)? Explain your choice.
A. Does a=25 and b=4?
B. Does a=25 and b=21?
C. Does a=4 and b=21?
D. Does a=21 and b=25?

I keep getting that a should equal 14 and I have no idea how to go about finding b. Can someone help please? Thanks!

Answer 1

focus at (–2, 0) and a vertex at (5, 0), so
a = 5 and c =-2
b^2= a^2-c^2 = 25 -(-2)^2 = 21
So equation is x^2/25 + b^2/21 = 1