Finding equation of hyperbola from asymptotes and foci

Hi I am very confused as to how this question actually works out...

I am asked to find the equation of a hyperbola with foci at (-3,-1) and (-3,9)

and asymptotes at y=(-3x/4)+(7/4) and y=(3x/4)+(25/4)

Every time I try to visualize this my foci are on a different side of the x-axis than my foci which completely throws all my thoughts out

I also don't particularly know how to get the equation when there is asymptotic shifts...

PLEASE HELP ME

Re: Finding equation of hyperbola from asymptotes and foci

have a look at this and see if it helps

Re: Finding equation of hyperbola from asymptotes and foci

Hello, calmo11!

Since the foci are oriented vertically, the hyperbola is "vertical": .

Its general equation is: .

. . where is the center and is the slope of the asymptotes.

The foci are and .

The center is the midpoint: .

The slope of the asymptotes is: .

Hence: .

Got it?

Re: Finding equation of hyperbola from asymptotes and foci

Thank you very much guys, I used romsek's link and the content on that site helped me heaps!