1998 AHSME Problem 23

The graphs of x^2 + y^2 = 4 + 12x + 6y and x^2 + y^2 = k + 4x + 12y intersect when k satisfies a \le k \le b, and for no other values of k. Find b-a.

\mathrm{(A) \ }5 \qquad \mathrm{(B) \ }68 \qquad \mathrm{(C) \ }104 \qquad \mathrm{(D) \ }140 \qquad \mathrm{(E) \ }144

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.