Let \( \mathbb{R} \) denote the set of all real numbers. Let \( z_{1}=1+2i \) and \( z_{2}=3i \) be two complex numbers, where \( i=\sqrt{-1} \). Let \( S=\{(x,y)\in \mathbb{R}\times \mathbb{R}: |x+iy-z_{1}|=2\,|x+iy-z_{2}|\} \).
Then which of the following statements is(are) TRUE?
