The locus of the points represented by |z+3|-|z-3|=6, where z is a complex number, is .

MHT CET 2025 Mathematics question

The locus of the points represented by , where z is a complex number, is .

(A)Circle with radius 1 unit
(B)Straight line with slope 1.
(C)Parabola with focus (1,0)
(D)X-axisCorrect

Answer: (D)

Solution

Let A(−3,0) and B(3,0); then for a point P. By the triangle inequality , i.e. , with equality only when P lies on line AB outside the segment, beyond B. Hence P lies on the X-axis (the ray

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Question ID VK-101840