Question

The region represented by $|z+a|+|z-a|<4a$ is ....

• A. Ellipse
• B. Parabola
• C. Interior of Ellipse
• D. Outer of Ellipse

Answer 1

The correct option is C Interior of Ellipse

$|z+a|:$ distance of 'z' from'-a'
$|z-a|:$ distance of 'z' from 'a'
$\therefore |z+a|+|z-a|<4a:$
represents the locus of 'z' such that the sum of its distance from two fixed point is less than or equal to a constant value i.e 4a.
thus of $|z+a|+|z-a|=4a:$ ellipse (By definition of ellipse)
$\therefore |z+a|+|z-a|<4a:$ represents all those points which lie inside this ellipse