Let
S_1 \equal{} \{ (x,y)\ | \ \log_{10} (1 \plus{} x^2 \plus{} y^2)\le 1 \plus{} \log_{10}(x \plus{} y)\}
and
S_2 \equal{} \{ (x,y)\ | \ \log_{10} (2 \plus{} x^2 \plus{} y^2)\le 2 \plus{} \log_{10}(x \plus{} y)\}.
What is the ratio of the area of S2 to the area of S1?
<spanclass=′latex−bold′>(A)</span>98<spanclass=′latex−bold′>(B)</span>99<spanclass=′latex−bold′>(C)</span>100<spanclass=′latex−bold′>(D)</span>101<spanclass=′latex−bold′>(E)</span>102