A circle of radius r passes through both foci of, and exactly four points on, the ellipse with equation x^{2}+16 y^{2}=16. The set of all possible values of r is an interval [a, b). What is a+b ?
Answer Choices
A. 5 \sqrt{2}+4
B. \sqrt{17}+7
C. 6 \sqrt{2}+3
D. \sqrt{15}+8
E. 12