Chắc là biểu thức vecto???
Gọi \(M\left(x;y\right)\Rightarrow\left\{{}\begin{matrix}\overrightarrow{MA}=\left(-x;-4-y\right)\\\overrightarrow{MB}=\left(-5-x;6-y\right)\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\overrightarrow{MA}+\overrightarrow{MB}=\left(-5-2x;2-2y\right)\\\overrightarrow{MA}-\overrightarrow{MB}=\left(5;-10\right)\end{matrix}\right.\)
\(\left|\overrightarrow{MA}+\overrightarrow{MB}\right|=\left|\overrightarrow{MA}-\overrightarrow{MB}\right|\)
\(\Leftrightarrow x^2+\left(y+4\right)^2+\left(x+5\right)^2+\left(y-6\right)^2=5^2+\left(-10\right)^2\)
\(\Leftrightarrow2x^2+10x+2y^2-4y-48=0\)
\(\Leftrightarrow x^2+5x+y^2-2y-24=0\)
\(\Leftrightarrow\left(x+\frac{5}{2}\right)^2+\left(y-1\right)^2=\frac{125}{4}\)
Quỹ tích M là đường tròn tâm \(I\left(-\frac{5}{2};1\right)\) bán kính \(R=\frac{5\sqrt{5}}{2}\)
