Let $\mathbb { R }$ denote the set of all real numbers. Let $z _ { 1 } = 1 + 2 i$ and $z _ { 2 } = 3 i$ be two complex numbers, where $i = \sqrt { - 1 }$. Let

$$S = \left\{ ( x , y ) \in \mathbb { R } \times \mathbb { R } : \left| x + i y - z _ { 1 } \right| = 2 \left| x + i y - z _ { 2 } \right| \right\}$$

Then which of the following statements is (are) TRUE?

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\begin{tabular}{|l|l|}
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(A) & $S$ is a circle with centre $\left( - \frac { 1 } { 3 } , \frac { 10 } { 3 } \right)$ \\
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(B) & $S$ is a circle with centre $\left( \frac { 1 } { 3 } , \frac { 8 } { 3 } \right)$ \\
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(C) & $S$ is a circle with radius $\frac { \sqrt { 2 } } { 3 }$ \\
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(D) & $S$ is a circle with radius $\frac { 2 \sqrt { 2 } } { 3 }$ \\
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\end{tabular}
\end{center}