Đáp án:
\(\left( {O'} \right):\,\,\,{\left( {x + 1} \right)^2} + {\left( {y - 2} \right)^2} = 4.\)
Giải thích các bước giải:
\(\begin{array}{l}
\left( O \right):\,\,{x^2} + {y^2} + 2x + 4y + 1 = 0\\
\Leftrightarrow \left( {{x^2} + 2x + 1} \right) + \left( {{y^2} + 4y + 4} \right) - 4 = 0\\
\Leftrightarrow {\left( {x + 1} \right)^2} + {\left( {y + 2} \right)^2} = 4\\
\Rightarrow \left( O \right)\,\,\,co\,\,tam\,\,\,I\left( { - 1; - 2} \right),\,\,\,ban\,\,kinh\,\,\,R = 2.\\
Goi\,\,\,I'\left( {a;\,\,b} \right)\,\,\,la\,\,diem\,\,\,doi\,\,\,xung\,\,\,cua\,\,\,I\left( { - 1; - 2} \right)\,\,\,qua\,\,\,truc\,\,\,Ox\\
\Rightarrow \left\{ \begin{array}{l}
a = - 1\\
b = 2
\end{array} \right. \Rightarrow I\left( { - 1;\,\,2} \right)\\
Goi\,\,\,\left( {O'} \right)\,\,\,la\,\,\,anh\,\,cua\,\,\,\left( O \right)\,\,\,\,qua\,\,\,phep\,\,\,doi\,\,xung\,\,truc\,\,Ox\\
\Rightarrow \left( {O'} \right)\,\,\,co\,\,tam\,\,\,I'\left( { - 1;\,\,2} \right)\,\,va\,\,ban\,\,\,kinh\,\,\,R = 2.\\
\Rightarrow \left( {O'} \right):\,\,\,{\left( {x + 1} \right)^2} + {\left( {y - 2} \right)^2} = 4.
\end{array}\)
