I have a graph of a hyperbola where the vertices are at (-3,0) and (3,0) and the center is (0,0). It needs to be written in a standard form

Question

(x-h)² / a² - (y-k)² / b²

Answer 1

center = (h,k) = (0,0)

vertices are (-a,0) and (a,0) = (-3,0) and (3,0)

a = 3

the hyperbola's equation is

(x-h)^2/a^2 - (y-k)^2/b^2 = 1

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

or

(bx)^2 -(3y)^2 = 9b^2

asymptotes are y=bx/3 and -bx/3

foci are (-c,0) and (c,0) where c^2 = a^2 + b^2 = 9 + b^2, c = square root of (9+b^2)