Can someone please explain to me how to get the 16 in this equation. I get how to get everything else but i don't know how to get the 16.

Question

A hyperbola with foci: (0,5) (0,-5)and vertices: (0,3) (0,-3). So i got y^2/9-x^2/16=1. but how do you get the 16?

Answer 1

center is at (0,0) so the form is:
y^2/a^2 -x^2/b^2 = 1

distance center to focus = 5 = sqrt(a^2+b^2)
distance center to vertex = 3 = a
so
5^2 = (3^2 + b^2)
25 = 9 + b^2
b^2 = 16

Answer 2

thanks man