Question

Cho A(1;2) tìm M trên trục Oy sao cho MA=5

Answer 1

Do M thuộc Oy nên tọa độ có dạng \(M\left(0;m\right)\)

\(\Rightarrow\overrightarrow{AM}=\left(-1;m-2\right)\)

\(\Rightarrow AM=\sqrt{\left(-1\right)^2+\left(m-2\right)^2}=\sqrt{m^2-4m+5}\)

\(MA=5\Leftrightarrow\sqrt{m^2-4m+5}=5\)

\(\Leftrightarrow m^2-4m-20=0\)

\(\Rightarrow\left[{}\begin{matrix}m=2+2\sqrt{6}\\m=2-2\sqrt{6}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}M\left(0;2+2\sqrt{6}\right)\\M\left(0;2-2\sqrt{6}\right)\end{matrix}\right.\)