Question

The region represented by $|z-1|+|z+1|\le 4$ is

• A. interior or ellipse
• B. exterior of a circle
• C. interior and boundary of an ellipse
• D. interior of a circle

Answer 1

Answer: (C)

interior and boundary of an ellipse

we have, $|z-z_0|+|z-z_1|=c$
is the equation of ellipse with $z_0$ and $z_1$ as focii
$|z-1|+|z+1|\le 4$ is the equation of all points lying inside and on an ellipse with focii (1,0) & (-1,0)