Complex Numbers and Quadratic Equations · Question 4

JEE Advanced 2025 Paper 1Multiple CorrectEasy📈 Topic in 17% papers+4−1

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?

S is a circle with centre (- 13, 103 )
S is a circle with centre ( 13, 83 )
S is a circle with radius 23
S is a circle with radius 2 23

Answer

(1) S is a circle with centre (- 13, 103 ), (4) S is a circle with radius 2 23

Solution

Square both sides: (x-1)2 + (y-2)2 = 4 [x2 + (y-3)2 ].

x2 - 2x + y2 - 4y + 5 = 4x2 + 4y2 - 24y + 36 3x2 + 3y2 + 2x - 20y + 31 = 0.

x2 + y2 + 23x - 203y + 313 = 0: centre (- 13, 103 ).

r2 = 19 + 1009 - 313 = 89 r = 2 23.

Answer: (A), (D)

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