Question

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

• A. circle
• B. on and inside circle
• C. on and inside an ellipse
• D. inside of ellipse

Answer 1

Answer: (C)

on and inside an ellipse

we know that equation
$|z-z_0|+|z-z_1|=c$
is the equation of an ellipse with $z_0$ & $z_1$ as focii
here $|z+i|+|z-i|=4$ is an equation of ellipse with (0,1) & (0,-1) as the focii the 'less than' sign represent all the points inside ellipse