Đáp án: D
Giải thích các bước giải:
$\begin{array}{l}
\left( C \right):{x^2} + {y^2} - 3x - y = 0\\
\Rightarrow \left( {{x^2} - 3x + \dfrac{9}{4}} \right) + {y^2} - \dfrac{1}{2}y + \dfrac{1}{4} = \dfrac{9}{4} + \dfrac{1}{4}\\
\Rightarrow {\left( {x - \dfrac{3}{2}} \right)^2} + {\left( {y - \dfrac{1}{2}} \right)^2} = \dfrac{5}{2}\\
\Rightarrow Tâm:I\left( {\dfrac{3}{2};\dfrac{1}{2}} \right);R = \sqrt {\dfrac{5}{2}} = \dfrac{{\sqrt {10} }}{2}\\
M\left( {1; - 1} \right) \in \left( C \right)\\
\Rightarrow \overrightarrow {MI} = \left( {\dfrac{1}{2};\dfrac{3}{2}} \right) \bot PTTT\\
\Rightarrow PTTT:\dfrac{1}{2}x + \dfrac{3}{2}y + c = 0\\
hay:x + 3y + 2c = 0\\
Do:M\left( {1; - 1} \right) \in PTTT\\
\Rightarrow 1 + 3.\left( { - 1} \right) + 2c = 0\\
\Rightarrow 2c = 2\\
\Rightarrow PTTT:x + 3y + 2 = 0
\end{array}$
