The equation of a hyperbola that opens upward and downward has
general equation



where (h,k) is the center, a = half the transverse axis,
b = half the conjugate axis.

(h,k) = (-5,-3)

The red vertical line is the transverse axis. It is 4 units long.
The semi-transverse axis is half the transverse axis, so a=2

The blue horizontal line is the conjugate axis. It is 12 units long.
The semi-transverse axis is half the conjugate axis, so b=6

So the equation of the hyperbola, which is what you want, is





The green rectangle is the "defining rectangle".  The slanted green
lines are the extended diagonals of the defining rectangle.  They are 
the asymptotes of the hyperbola.

Edwin