How do you write an equation for the hyperbola with vertices (0,2) and (0,-2) and foci at (0,9) and (0,-9)?
Center C bisects the line joining the vertices
So C is at the origin.
The distance between the vertices is the transverse axis 2a = 4.
So, a = 2.
The distance between the foci = 2a X eccentricity (e).
So, 4e = 18. e = 9/2.
The semi-transverse axis
Now, the equation of the hyperbola takes the standard form