G2.1 If $\frac{137}{a}=0.1 \dot{2} 3 \dot{4}$, find the value of $a$.
G2.2 If $b=1999 \times 19981998-1998 \times 19991999+1$, find the value of $b$.
G2.3 If the parametric equation $\left\{\begin{array}{l}x=\sqrt{3-t^{2}} \\ y=t-3\end{array}\right.$ can be transformed into $x^{2}+y^{2}+c x+d y+6=0$, find the values of $c$ and $d$.
$\begin{array}{l}\frac{137}{a}=0.123 \dot{4}=0.1+\frac{234}{9990}=\frac{999+234}{9990}=\frac{1233}{9990}=\frac{137}{1110} \\ a=1110 \\ b=1999 \times 1998 \times 1001-1998 \times 1999 \times 1001+1=1 \\ (1)^{2}+(2)^{2}: x^{2}+y^{2}=-6 t+12=-6(y+3)+12 \\ c=0, d=6\end{array}$