Đường tròn (C): \(\left\{{}\begin{matrix}I\left(-1;1\right)\\R=5\end{matrix}\right.\)
Gọi \(\Delta:ax+by+c=0\) (\(a;b\ne0\))
\(M\in\Delta\Rightarrow9a-4b+c=0\)
\(\Leftrightarrow c=4b-9a\)
Do \(\Delta\) là tiếp tuyến của (C) \(\Rightarrow d_{\left(I,\Delta\right)}=R\)
\(\Leftrightarrow\dfrac{\left|-a+b+c\right|}{\sqrt{a^2+b^2}}=5\) \(\Leftrightarrow\dfrac{\left|-a+b+4b-9a\right|}{\sqrt{a^2+b^2}}=5\)
\(\Leftrightarrow\left(5b-10a\right)^2=25\left(a^2+b^2\right)\)
\(\Leftrightarrow-3a^2+4ab=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3a=4b\\a=0\left(L\right)\end{matrix}\right.\)
3a=4b
Chọn a=4;b=3 =>c=-24
=>\(\Delta:4x+3y-24=0\)
\(d_{\left(N;\Delta\right)}=\dfrac{\left|4.2020+3.2021-24\right|}{\sqrt{4^2+3^2}}=2823,8\)
