Question

Write the equation of a hyperbola with vertices (0, -4) and (0, 4) and foci (0, -5) and (0, 5).

Answer 1

well the center would be the origin (0,0)
a = 4
b=?
c = 5

a^2 + b^2 = c^2
--> b^2 = 25-16 = 9
--> b = 3

equation:
\[\frac{y^{2}}{16} - \frac{x^{2}}{9} = 1\]

Answer 2

since vertices/foci are on vertical axis, that is why the y^2 goes first

Answer 3

D

Answer 4

thank you! :)