AMC 12A 2006 Problem 21

Let

S_{1}=\left\{(x, y) \mid \log _{10}\left(1+x^{2}+y^{2}\right) \leq 1+\log _{10}(x+y)\right\}

and

S_{2}=\left\{(x, y) \mid \log _{10}\left(2+x^{2}+y^{2}\right) \leq 2+\log _{10}(x+y)\right\}

What is the ratio of the area of S_{2} to the area of S_{1} ?

Answer Choices
A. 98
B. 99
C. 100
D. 101
E. 102