Phương trình đường tròn \( \left( C \right): \, \,{{x}^{2}}+{{y}^{2}}-2x-8=0. \, \,I \left( 1;4 \right). \, \,{{V}_{ \left( I; \frac{1}{3} \right)}}: \, \, \left( C \right) \mapsto \left( C' \right) \). Tìm phương trình \( \left( C' \right) \).
A.\(\left( C' \right):\,\,{{x}^{2}}+{{y}^{2}}-2x-\frac{16}{5}y+\frac{64}{9}=0\).
B.\(\left( C' \right):\,\,{{x}^{2}}+{{y}^{2}}-4x-\frac{16}{3}y+\frac{64}{9}=0\).
C.\(\left( C' \right):\,\,{{x}^{2}}+{{y}^{2}}-2x-\frac{16}{3}y+\frac{64}{9}=0\).
D.\(\left( C' \right):\,\,{{x}^{2}}+{{y}^{2}}-2x-\frac{14}{3}y+\frac{4}{9}=0\).