Câu hỏi 11

\(\left( C \right):{\left( {x - 3} \right)^2} + {\left( {y + 1} \right)^2} = 5\) có tâm \(A\left( {3; - 1} \right)\), bán kính \(R = \sqrt 5 \)

Phép vị tự tỉ số \(k =  - 2 \Rightarrow {R_{\left( {C'} \right)}} = \left| { - 2} \right|.\sqrt 5  = 2\sqrt 5 \)

\(\overrightarrow {IA'}  = \left( { - 2} \right).\overrightarrow {IA} \)

Gọi \(A'\left( {x;y} \right)\)\( \Rightarrow \overrightarrow {IA'} \left( {x - 1;y - 2} \right);\,\,\,\overrightarrow {IA} \left( {2; - 3} \right)\)

\(\begin{array}{l} \Rightarrow \left\{ \begin{array}{l}x - 1 = \left( { - 2} \right).2\\y - 2 = \left( { - 2} \right).\left( { - 3} \right)\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}x =  - 3\\y = 8\end{array} \right.\\ \Rightarrow \left( {C'} \right):{\left[ {x - \left( { - 3} \right)} \right]^2} + {\left( {y - 8} \right)^2} = {\left( {2\sqrt 5 } \right)^2}\\ \Leftrightarrow {\left( {x + 3} \right)^2} + {\left( {y - 8} \right)^2} = 20\end{array}\)

Chọn C.