Question

The locus represented by the equation , |z-1| + |z+1| = 2 is :

• A. An ellipse with foci (1, 0) and (–1, 0)
• B. One of the family of circles passing through the points of intersection of the circles $|z+1|=1$
• C. The radical axis of the circles $|z-1|=1$ and $|z+1|=1$
• D. The portion of the real axis between the points (1, 0) and (–1, 0)

Answer 1

The correct option is D

The portion of the real axis between the points (1, 0) and (–1, 0)

$|z-1|+|z+1|=2$

Hence, the locus is the portion of the real axis between (-1,0) and (1,0) as the distance between both the points is 2.