$\begin{array}{l} \left( C \right):{x^2} + {y^2} - 2x + 4y - 4 = 0\\ \Leftrightarrow {\left( {x - 1} \right)^2} + {\left( {y + 2} \right)^2} = 9\\ \Rightarrow I\left( {1; - 2} \right),R = 3\\ {Q_{\left( {O,\dfrac{\pi }{2}} \right)}}\left( C \right) = C'\\ \Rightarrow {Q_{\left( {O,\dfrac{\pi }{2}} \right)}}\left( I \right) = I'\\ \Rightarrow I'\left( {2;1} \right),R' = R = 3\\ \Rightarrow {Q_{\left( {O,\dfrac{\pi }{2}} \right)}}\left( C \right) = C':{\left( {x - 2} \right)^2} + {\left( {y - 1} \right)^2} = 9 \end{array}$
