SOLUTION: What is the standard form of a hyperbola with the given conditions foci at (-13,0) (13,0) vertices at (12,0) (-12,0)

Question 947817: What is the standard form of a hyperbola with the given conditions
foci at (-13,0) (13,0)
vertices at (12,0) (-12,0)
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The transverse axis (the segment connecting the vertices) is a segment of the x-axis,
so the transverse axis of this hyperbola is "horizontal" (in the same direction as the x-axis).
The center of the hyperbola is the midpoint of the transverse axis,
and the midpoint of the segment connecting (12,0) and (-12,0) is (0,0), the origin,
so this hyperbola is centered at the origin, with a horizontal transverse axis.
A hyperbola centered at the origin, with a horizontal transverse axis has an equation of the form
, with some positive numbers and .
With that equation, we get
--> --> ,
meaning that the points

and

are the vertices,
so we know that .
We also know that the foci are at a distance from the center,
and that .
In the case of this hyperbola, obviously ,
and knowing that ,
we can substitute the values for and into ,
to get the equation , which will give us .
-->-->-->-->
.
With values for and ,
we can substitute into ,
to get the equation for our hyperbola as
or

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