Find the equation of the hyperbola centered at the origin with vertices (0,8) and (0,−8) and asymptotes y=±23x.

Answer 1

Since center is (0, 0) and the vertices are at a distance 8 from the center on the y axis, the equation is like

................. (1)

Asymptotes are

So = 23.

b = 8/23 . Substitute this b in equation (1).