Question

The region of Argand diagram defined by $|z-1|+|z+1|\le 4$ is

• A. interior of an ellipse
• B. exterior of a circle
• C. interior and boundary of an ellipse
• D. none of these

Answer 1

The correct option is C interior and boundary of an ellipse

Here, $|z_1-z_2|=|1-(-1)|=2$ and $a=4$

$\therefore |z_1-z_2|<a$
Hence region represented by $|z-1|+|z+1|\le 4$ is an interior and boundary of an ellipse.