JEE Advance - Mathematics (2025 - Paper 1 Online - No. 7)
Let 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?
S is a circle with centre $\left(-\frac{1}{3}, \frac{10}{3}\right)$
S is a circle with centre $\left(\frac{1}{3}, \frac{8}{3} \right)$
S is a circle with radius $\frac{\sqrt{2}}{3}$
S is a circle with radius $\frac{2\sqrt{2}}{3}$
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