(D) for me
(x-a)^2 + (y-b)^2 = 16 is the formula of a circle with its center at (a,b) and its radius equal to sqrt(16) = 4.
Thus, all we have to know is wether a is far enough on the X axis to not create 1 or 2 intersects between the circrle and the Y axes.
a^2 > 16
<=> a <4> 4.
Bingo! in other word, |a| is superior to the radius that is 4, creating no intersects with the Y axes.
a = |b| + 5
<b>= 0 (by definition), we have:
a -5 >=5
.... |a| is again greater than the radius 4.