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} \text {. 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?
Select ALL correct options:
A
S is a circle with centre $\left(-\frac{1}{3}, \frac{10}{3}\right)$
B
S is a circle with centre $\left(\frac{1}{3}, \frac{8}{3}\right)$
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