Question

Find an equation for the hyperbola that satisfies the given conditions.
Foci (0, ±12), vertices (0, ±6)

Answer 1

center at (0,0)
c = 12
a = 6
a^2 +b^2 = c^2
36 + b^2 = 144
b^2 = 108
Equation:
\[\frac{y^{2}}{36}-\frac{x^{2}}{108} = 1\]