Mathematics - Circle Question with Solution | TestHub

Unit circles $S_1,S_2$ have centres $(0,0),(1,0)$. Unit circle $S_3$ passes through both centres and lies above the $x$-axis. A common tangent of $S_1,S_3$ is $ax+by+2=0$. Let $P$ be the ordinate of the centre of $S_3,Q=a,R=a^2-b$, and $S$ be the abscissa of the centre of $S_3$. Which option correctly matches $P,Q,R,S$ with the values $1/2,\sqrt{3}/2,\sqrt{3},4$ ?