Gọi \(M\left(m;0\right)\Rightarrow\left\{{}\begin{matrix}\overrightarrow{AM}=\left(m+3;-2\right)\\\overrightarrow{BM}=\left(m-4;-3\right)\end{matrix}\right.\)
MAB vuông tại M \(\Leftrightarrow AM\perp BM\)
\(\Leftrightarrow\overrightarrow{AM}.\overrightarrow{BM}=0\)
\(\Leftrightarrow\left(m+3\right)\left(m-4\right)+6=0\)
\(\Leftrightarrow m^2-m-6=0\Rightarrow\left[{}\begin{matrix}m=3\\m=-2\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}M\left(3;0\right)\\M\left(-2;0\right)\end{matrix}\right.\)
b. Gọi \(N\left(0;y\right)\Rightarrow\left\{{}\begin{matrix}\overrightarrow{AN}=\left(3;y-2\right)\\\overrightarrow{BN}=\left(-4;y-3\right)\end{matrix}\right.\)
\(NA=NB\Rightarrow NA^2=NB^2\)
\(\Rightarrow9+\left(y-2\right)^2=16+\left(y-3\right)^2\)
\(\Rightarrow2y=12\Rightarrow y=6\)
\(\Rightarrow N\left(0;6\right)\)
