The horizontal blue line I added:
The transverse axis extends from vertex (-7,-3/2) to vertex (-1,-3/2)
so the transverse axis is 6 units long. The semi-transverse axis is
'a' which is half of 6 or a=3.

The vertical blue line that I added:
The conjugate axis extends from midpoint of top side to midpoint of 
bottom side of defining rectangle, from (4,-1) to vertex (-4,-2)
so the conjugate axis is 1 units long. The semi-conjugate axis is
'b' which is half of 1 or b=1/2.

The center is (h,k)=(-4,-3/2) so the equation becomes in standard form



Now if you do some work on that, you'll 

end up with this general form: 



Edwin