question_answer

If z satisfies\[\left| z-1 \right|+\left| z+1 \right|=2\], then locus of z is

A) A straight line passing through \[z=1\]& \[z=-1\]

B) Circle

C) A line segment

D) Ellipse

Correct Answer: A

Solution :

[a] \[\left| z-1 \right|\] and \[\left| z+1 \right|\] represent distance of complex No. z from 1 and - 1 respectively in the Argand plane Now distance between \[z=-1\] and \[z=1\]is 2 & \[\left| z-1 \right|+\left| z+1 \right|=2\] so locus will be line segment joining - 1 & 1.