The combined equation of the direct common tangents of the circles $x^2+y^2-2x-2y-2=0$ and $x^2+y^2+4x+6y+12=0$ is 

$$\begin{gathered} C_1=(1, 1) , {\mathrm{r}}_1=\sqrt{4}=2 \\ {C}_2=(-2, -3) , {\mathrm{r}}_2=\sqrt{1} \\ \Rightarrow {\mathrm{r}}_2=1 \\ \mathrm{External} \mathrm{centre} \mathrm{of} \mathrm{similitude}=(-5,-7) \\ \mathrm{equation} \mathrm{of} \mathrm{combined} \mathrm{equation} \mathrm{of} \mathrm{direct} \mathrm{common} \mathrm{tangent} \mathrm{is} {{\mathrm{S}}_1}^2=\mathrm{S}.{\mathrm{S}}_{11} \\ \mathrm{OR} \\ \mathrm{verify} \mathrm{the} \mathrm{options} \mathrm{which} \mathrm{is} \mathrm{passing} \mathrm{through} \mathrm{the} \mathrm{point}(-5,-7 ) \end{gathered}$$