Find an equation for the hyperbola

Question

Find an equation for the hyperbola that satisfies the given conditions:

 

Vertices (0±4)

 

Asymptotes y=±( 1/2)x

Answer 1

Since the vertices are centered at the origin and the x-coordinates are both 0, the equation of the hyperbolae are

y^2/a^2 - x^2/b^2 = 1

From the vertex location, a = 4

The slope of the asymptotes is a/b

4/b = 1/2

cross-multiplying, b = 4*2 

b = 8

y^2/4^2 - x^2/8^2 = 1, or

y^2/16 - x^2/64 = 1