On plotting the diagram of given data we get,

Now we know that common chord is given by $S_1-S_2=4x+4y+5=0$

Now we know common chord is bisected by line joining the centre ,

So assuming line joining the centres of circle is dividing the common chord in $\lambda :1$,

So coordinate of centre of circle $S$ is given by $x=\frac{2}{\lambda +1} \& y=\frac{-2\lambda }{\lambda +1}$

Now centre will lie on the common chord so,

$4\times \frac{2}{\lambda +1} +4\times \frac{-2\lambda }{\lambda +1}+5=0$

$\Rightarrow \lambda =\frac{13}{3}$

So absicissa will be $\frac{2}{\lambda +1}=\frac{3}{8}$