Question 21
Let
$$
\tiny S_1 = \{(x, y) \mid \log_{10}(1 + x^2 + y^2) \le 1 + \log_{10}(x + y)\}
$$
and
$$
\tiny S_2 = \{(x, y) \mid \log_{10}(2 + x^2 + y^2) \le 2 + \log_{10}(x + y)\}.
$$
What is the ratio of the area of $S_2$ to the area of $S_1?$
$$
\tiny S_1 = \{(x, y) \mid \log_{10}(1 + x^2 + y^2) \le 1 + \log_{10}(x + y)\}
$$
and
$$
\tiny S_2 = \{(x, y) \mid \log_{10}(2 + x^2 + y^2) \le 2 + \log_{10}(x + y)\}.
$$
What is the ratio of the area of $S_2$ to the area of $S_1?$