$\begin{array}{l}
A\left( { - 3;\,\,1} \right);\,\,\,\overrightarrow v = \left( {2;\,\, - 4} \right)\\
\left( C \right):\,\,{\left( {x - 5} \right)^2} + {y^2} = 6 \Rightarrow I\left( {5;\,0} \right),\,\,\,R = \sqrt 6 .\\
\Rightarrow \overrightarrow {IA} = \left( { - 8;\,\,1} \right) = - \left( {8; - \,1} \right).\\
\Delta \,\,\,la\,\,duong\,\,tiep\,\,tuyen\,\,cua\,\,\,\left( C \right)\,\,tai\,\,A\\
\Rightarrow \Delta \,\,nhan\,\,\overrightarrow {IA} \,\,\,lam\,\,\,VTPT.\\
\Rightarrow \Delta :\,\,\,8\left( {x + 3} \right) - \left( {y - 1} \right) = 0 \Leftrightarrow 8x - y + 25 = 0.\\
Goi\,\,\,A'\left( {a;\,\,b} \right)\,\,la\,\,anh\,\,cua\,\,A\,\,qua\,\,{T_{\overrightarrow v }}\\
\Rightarrow \left\{ \begin{array}{l}
a = - 3 + 2\\
b = 1 - 4
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = - 1\\
b = - 3
\end{array} \right. \Rightarrow A'\left( { - 1; - 3} \right).\\
d\,\,la\,\,\,anh\,\,cua\,\,\Delta \,\,qua\,\,{T_{\overrightarrow v }} \Rightarrow d:\,\,\,8x - y + c = 0\,\,\,\left( {c \ne 25} \right)\\
\Rightarrow A' \in d' \Rightarrow 8.\left( { - 1} \right) + 3 + c = 0\\
\Leftrightarrow c = 5\,\,\left( {tm} \right)\\
\Rightarrow d':\,\,8x - y + 5 = 0.
\end{array}$
