Question

A hyperbola has vertices (0,-6) and (0,6) and asymptotes y=3/4x and y=-3/4x. The center is (0,0).

In what direction is this hyperbola oriented?

Answer 1

Center of the hyperbola is the midpoint of the vertices.
Midpoint of (0,-6) and (0,6) is (0,0)

The transverse axis is the x-axis.
Equation is x^2 / a^2 - y^2 / b^2 = 0

Asymptote = y^2 = (b^2/a^2) x^2
+/- (b/a)
b/a = 3/4
b=3
a=4

x^2 / 16 - y^2 / 9 = 1

Answer 2

thank you very much! :)