Gọi pt (P) dạng \(ax+by+cz+d=0\)
Do (P) qua A và B nên: \(\left\{{}\begin{matrix}a+b+c+d=0\\a+d=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a+d=0\\b+c=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}d=-a\\c=-b\end{matrix}\right.\) \(\Rightarrow\left(P\right):ax+by-bz-a=0\)
Mặt cầu (S) tâm \(I\left(1;1;-2\right)\) bán kính R=2
(P) tiếp xúc (S) \(\Rightarrow d\left(I;\left(P\right)\right)=R\)
\(\Rightarrow\dfrac{\left|a+b+2b-a\right|}{\sqrt{a^2+2b^2}}=2\) \(\Rightarrow9b^2=4\left(a^2+2b^2\right)\)
\(\Rightarrow4a^2-b^2=0\Rightarrow\left[{}\begin{matrix}b=2a\\b=-2a\end{matrix}\right.\)
Chọn \(a=1\Rightarrow\left[{}\begin{matrix}a=2\\b=-2\end{matrix}\right.\)
Có 2 mp thỏa mãn: \(\left[{}\begin{matrix}x+2y-2z-1=0\\x-2y+2z-1=0\end{matrix}\right.\)
