Find the equation of the hyperbola whose vertices are at (-1,-5) and (-1,1) with a focus at (-1,-7).
So far I have the center at (-1,-2) and part of the equation is (y+2)^2 - (x+1)^2 but do not know how to figure a^2, b^2, or c^2.
Hmmm. I don't know what you mean by c.
(y+2)2/a2 -(x+1)2/b2 = 1
You have two points for x,y, that should give you two equation to solve for a, b.
center to vertex = a = 3
center to focus = sqrt(a^2+b^2) = 5
so 9+b^2 = 25
b = 4