How do you write the equation of the hyperbola given Foci: (0,-9),(0,9) and vertices (0,-3sqrt5), (0,3sqrt5)?
Because it is the y coordinate that is changing for the given points, use the vertical transverse axis form:
Using the given points, write the following equations:
To obtain the value of k, add equations  and :
To obtain the value of a, substitute 0 for k into equation :
Substitute the known values of "k" and "a" into equation 6 and solve for b:
Substitute the known values into equation :
Here is a graph of equation  with vertices and foci: