Question

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.

Answer 1

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.