I'll be probably too late, because alle the big shots are online, but nevertheless I'l give it a try:
With a circle in the x-y-plane you have 2 different equations:
You can easily transform (1) into (2) by expanding the brackets and collecting the constants.
Correct: The h-value indicates a translation in x-direction, the k-value indicates a move in y-direction.
h<0: move left, h>0: move right.
k<0: move up, k>0: move down
If you use another equation of the circle, the last properties may change, be careful with those signs in the brackets.