Posted by Lucy on Sunday, October 12, 2008 at 2:00pm.
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.
Help please....

PreCalculus  bobpursley, Sunday, October 12, 2008 at 2:27pm
Hmmm. I don't know what you mean by c.
(y+2)^{2}/a^{2} (x+1)^{2}/b^{2} = 1
You have two points for x,y, that should give you two equation to solve for a, b.

PreCalculus  Damon, Sunday, October 12, 2008 at 2:31pm
center to vertex = a = 3
center to focus = sqrt(a^2+b^2) = 5
so 9+b^2 = 25
b = 4
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