SOLUTION: Write an equation for the hyperbola with vertices (2,5),(2,-3) and conjugate axis of length 10

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Question 1112780: Write an equation for the hyperbola with vertices (2,5),(2,-3) and conjugate axis of length 10
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
Your hyperbola has one vertex above the other, both on the vertical line ,
so we say it has a vertical transverse axis.
That hyperbola, with its asymptotes and transverse axis would look like this:
.
Hyperbolas, like ellipses, have constants , , and ,
that determine their shapes, and their equations.
Adding those constant, the conjugate axis, and the foci, we have
, with equation .
In your ellipse the distance between the vertices is ,
so .
The center is the midpoint of the transverse axes,
with like the vertices) and .
The conjugate axis length is , so .
Plugging all those numbers into the equation "formula" above,
or .

For this problem, you do not need ,
which is the focal distance (the distance from the center to a focus).
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