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Complex Numbers question

2025 · Shift 1 · Q23

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PYQ Library
JEE Advanced
Mathematics
Complex Numbers
2025 · Shift 1 · Q23

Complex Numbers question

2025 · Shift 1 · Q23

JEE AdvancedMathematicsComplex NumbersMultiple correct+4 / −2

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?

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

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