We plot the two vertices and the center which is the midpoint
between them (2,-3), and sketch the hyperbola approximately, which must 
open up and down.



Since the hyperbola opens upward and downward, it has the equation:



The center is (h,k) = (2,-3), the midpoint between vertices, and 
a = 2, the distance between the center and a vertex.

So we have everything but b







If you have studied the formula for the length of the
latus rectum which is , we can use that to 
find b:





we have the equation




That's the standard equation.  The general equation can be 
gotten by multiplying through by LCD=12, squaring the
binomials and simplifying: 



There is another way to get this answer if you haven't
studied the latus rectum formula.  Let me know in the 
thank-you note form below if you haven't studied that 
formula, and I'll show you how to find b without using 
it.

Edwin