Question

Using the information given below write the equation of the hyperbola:

The transverse axis of the hyperbola lies on the line y=–3 and has length 6; the conjugate axis lies on the line x=2 and has length 8.

Answer 1

transverse axis y = -3
so, (x-h)^2/a^2 - (y+3)^2/b^2 = 1
transverse axis has length 6, so a=3
(x-h)^2/9 - (y+3)^2/b^2 = 1
conjugate axis x=2, so h=2
(x-2)^2/9 - (y+3)^2 = 1
conjugate axis has length 8, so b=4
(x-2)^2/9 - (y+3)^2/16 = 1

wikipedia has a thorough article on hyperbolas.
But I'm sure all this is in your text as well.