(S) có tâm $I\in Ox\Rightarrow I\left( t;0;0 \right),$ $\left( t\ge 0 \right)\Rightarrow \overline{MI}=\left( t-1;1;-2 \right)\Rightarrow MI=\sqrt{{{\left( t-1 \right)}^{2}}+1+4}$ $=\sqrt{{{t}^{2}}-2t+6}$.

Ta có (S) tiếp xúc với (P) tại M $\Leftrightarrow d\left( I;\left( P \right) \right)=R=MI\Leftrightarrow \frac{\left| t-6 \right|}{\sqrt{6}}=\sqrt{{{t}^{2}}-2t+6}$ $\Leftrightarrow {{t}^{2}}-12t+36=6\left( {{t}^{2}}-2t+6 \right)\Leftrightarrow 5{{t}^{2}}=0\Leftrightarrow t=0\Rightarrow I\left( 0;0;0 \right)$, $R=\sqrt{6}\Rightarrow \left( S \right):{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=6$.