Đáp án:
\(\left( {C'} \right):{\left( {x - \frac{5}{2}} \right)^2} + {y^2} = 4\)
Giải thích các bước giải:
$\begin{array}{l}
\left( C \right)\,co\,tam\,I\left( {3; - 2} \right),R = 4\\
I' = {V_{\left( {A,\frac{1}{2}} \right)}}\left( I \right) \Leftrightarrow \overrightarrow {AI'} = \frac{1}{2}\overrightarrow {AI} \\
\Leftrightarrow \left\{ \begin{array}{l}
{x_{I'}} - 2 = \frac{1}{2}\left( {3 - 2} \right)\\
{y_{I'}} - 1 = \frac{1}{2}\left( { - 1 - 1} \right)
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
{x_{I'}} = \frac{5}{2}\\
{y_{I'}} = 0
\end{array} \right. \Rightarrow I'\left( {\frac{5}{2};0} \right)\\
\left( {C'} \right)\,co\,tam\,I'\left( {\frac{5}{2};0} \right),ban\,kinh\,R' = \frac{1}{2}R = 2\\
\Rightarrow \left( {C'} \right):{\left( {x - \frac{5}{2}} \right)^2} + {y^2} = 4
\end{array}$
