the equation for a hyperbola is (x-h)^2/a^2 - (y-k)^2/b^2 = 1 if the transverse axis is horizontal and (y-k)^2/a^2 - (x-h)^2/b^2 = 1 if the transverse axis is the vertical axis.
The transverse axis it eht line segment connecting the vertices. The foci are located c units from the center, where c^2 = a^2 + b^2. The center, vertices and foci all lie along the transverse axis. The hyperbola opens along the transverse axis as well.