SOLUTION: Find an equation for the hyperbola with C(2,4), foci F1(2,1) and F2(2,7), and vertices V1(2,6) and V2(2,2)

We plot those points:



It's a "vertical" hyperbola, opening up and down, like this: 



so its equation is 
of the form:



The center (h,k) is C(2,4) so h=2 and k=4, so, substituting:



"a" is the distance from the center to the vertex.
The distance from C(2,4) to V1(2,6) is 2 units and
the distance from C(2,4) to V2(2,2) is also 2 units,
so a=2.  So substituting:




"c" is the distance from the center to the focus.
The distance from C(2,4) to F1(2,1) is 3 units and
the distance from C(2,4) to F2(2,7) is also 3 units,
so c=3.  So substituting:

We must calculate b using the Pythagorean relation for hyperbolas:







Substituting b²=5

 

Edwin