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= \{(x, y) \in \mathbb{R} \times \mathbb{R}:{| x+i y-z_1 |}=2{| x+i y-z_2 |}\}. Then which of the following statements is (are) TRUE? [JEE Adv 2025 P1]

S is a circle with centre (-\frac{1}{3}, \frac{10}{3})

S is a circle with centre (\frac{1}{3}, \frac{8}{3})

S is a circle with radius {\sqrt{2}}/{3}

S is a circle with radius {2 \sqrt{2}}/{2}

JEE Advanced 2025 Paper 1

Section: Mathematics

Question : 7 of 48

Marks: +1, -0

Let ℝ denote the set of all real numbers. Let z1=1+2i and z2=3i be two complex numbers, where i=√−1. Let S={(x,y)∈ℝ×ℝ:|x+iy−z1|=2|x+iy−z2|}.
Then which of the following statements is (are) TRUE?

[JEE Adv 2025 P1]

S is a circle with centre (−‌
1
3
,‌
10
3
)
S is a circle with centre (‌
1
3
,‌
8
3
)
S is a circle with radius ‌
√2
3
S is a circle with radius ‌
2√2
2

Validate

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