Question 1068144: Write the equation of a hyperbola with vertices at (-3, 0) and (3, 0) and co-vertices (0, 5) and (0, -5).
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The center of a hyperbola (or of an ellipse) is the midpoint of the segment connecting the vertices.
In this case, the center is the point halfway between (-3,0) and (3,0) .
That center is point (0,0), the origin.
Hyperbolas centered at the origin have the simplest equations.
They are equations of the form
 or  .
The term with  in the denominator cannot be zero.
It has to be at least  .
For example, in , it must be true that  ,
so it must be true that  <--->  ,
and that makes (-a,0) and (a,0) the vertices.
The points (0,-b) and (0,b), which are not part of the hyperbola, are called the co-vertices.
The hyperbola in this problem is exactly that kind of hyperbola, with  ,
and equation
 or  .
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