AMC 12 2006a Problem 21

Let

$S_1=\{(x,y)|\log_{10}(1+x^2+y^2)\le 1+\log_{10}(x+y)\}$

and

$S_2=\{(x,y)|\log_{10}(2+x^2+y^2)\le 2+\log_{10}(x+y)\}$.

What is the ratio of the area of $S_2$ to the area of $S_1$?

$\mathrm{(A) \ } 98 \mathrm{(B) \ } 99 \mathrm{(C) \ } 100 \mathrm{(D) \ } 101 \mathrm{(E) \ } 102$