a: Thay x=2 và y=-1 vào (d), ta được:
2(m-2)+5=-1
=>2(m-2)=-6
=>m-2=-3
=>m=-1
b: (d): y=(m-2)x+5
=>(m-2)x-y-5=0
Khoảng cách từ O đến (d) là:
\(d\left(O;\left(d\right)\right)=\dfrac{\left|0\left(m-2\right)+0\left(-1\right)-5\right|}{\sqrt{\left(m-2\right)^2+\left(-1\right)^2}}=\dfrac{5}{\sqrt{\left(m-2\right)^2+1}}\)
Để d(O;(d))=3 thì \(\dfrac{5}{\sqrt{\left(m-2\right)^2+1}}=3\)
=>\(\sqrt{\left(m-2\right)^2+1}=\dfrac{5}{3}\)
=>\(\left(m-2\right)^2+1=\dfrac{25}{9}\)
=>\(\left(m-2\right)^2=\dfrac{16}{9}\)
=>\(\left[{}\begin{matrix}m-2=\dfrac{4}{3}\\m-2=-\dfrac{4}{3}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}m=\dfrac{10}{3}\\m=\dfrac{2}{3}\end{matrix}\right.\)
