A circle of radius r passes through both foci of, and exactly four points on, the ellipse with equation x2+16y2=16. The set of all possible values of r is an interval [a,b). What is a+b?<spanclass=′latex−bold′>(A)</span>52+4<spanclass=′latex−bold′>(B)</span>17+7<spanclass=′latex−bold′>(C)</span>62+3<spanclass=′latex−bold′>(D)</span>15+8<spanclass=′latex−bold′>(E)</span>12