You can put this solution on YOUR website! A good way to start is to write down the standard form of the equation for a hyperbola. The transverse axis is vertical in this case since it passes through both vertices. (Plot the two vertices on a piece of graph paper if you don’t see why.)
The standard equation for a hyperbola with a vertical transverse axis is:
The point (h,k) is the center of the hyperbola; it is the midpoint of the line segment between the two vertices at (2,3). This means that h=2 and k=3.
The parameter a is the distance from the center to each vertex. So, . (Plot the center on your graph if you don’t see why.)
The length of the conjugate axis is 2b. We are told that the conjugate axis is 6 units, so b=6/2=3.
Putting this all together, we have the equation,
Simplify:
