Write the equation of the hyperbola whose center is at the origin and has a vertical transverse axis. the equations of the asymptotes are 6x+2y=0 and 6x-2y=0.

 I'll tell you the rule first: 

The general form of the hyperbola having a vertical axis and centered at the origin is: 

(y/a)^2 ‑ (x/b)^2 = 1 

Asymptotes: 

y= ±(a/b)x 

Or (y/a)^2 - (x/b)^2 = 0 

So in your problem the asymptotes are: 

2y ± 6x = 0 

2y = ±6x 

y = ±(3/2)x 

So, a=3 b=2 

The equations are: 

(y/3)^2 - (x/2)^2 = 1 

(y^2)/8 - (x^2)/4 = 1 

Hope it helps you.