Gọi phương trình d: \(ax+by+c=0\)
Do d qua M nên: \(6a+b+c=0\Rightarrow c=-6a-b\)
Phương trình d: \(ax+by-6a-b=0\)
Do d tiếp xúc (C) \(\Rightarrow d\left(I;d\right)=R\)
\(\Rightarrow\frac{\left|a+2b-6a-b\right|}{\sqrt{a^2+b^2}}=2\sqrt{2}\) \(\Leftrightarrow\left|b-5a\right|=\sqrt{8a^2+8b^2}\Leftrightarrow\left(b-5a\right)^2=8a^2+8b^2\)
\(\Leftrightarrow17a^2-10ab-7b^2=0\Rightarrow\left[{}\begin{matrix}a=b\\b=-\frac{17}{7}a\end{matrix}\right.\)
Có 2 pt thỏa mãn:
\(\left[{}\begin{matrix}ax+ay-6a-a=0\\ax-\frac{17}{7}ay-6a+\frac{17}{7}a=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x+y-7=0\\7x-17y-25=0\end{matrix}\right.\)
