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

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Answer 1 · 2017-01-24T16:12:21

#y^2-x^2=9#. See vertices-inclusive graph.

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,

#A1xxA2=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 #(0, +-3)# is 9.