# How do you find the equation of the hyperbola with center at the origin and vertices (0,+-3) and asymptotes y=+-3x?

Jan 24, 2017

${y}^{2} - {x}^{2} = 9$. See vertices-inclusive graph.

#### Explanation:

graph{(y^2-x^2-9)(x^2+(y-3)^2-.01)(x^2+(y+3)^2-.01)=0 [-10, 10, -5, 5]} Use that if A1 = 0 and A2 = 0 are the equations to the asymptotes,

$A 1 \times A 2 = C$ represents the family of hyperbolas, having

A1xxA2=0 as its asymptotes. C is called the parameter for the

family.

Here, it is

(y-3x)(y+3x)=C, and

C for the rectangular hyperbola through $\left(0 , \pm 3\right)$ is 9.