Question

If the equation $|z-a|+|z-b|=3$ represents an ellipse and $a,b\in R$, (where $a$ is fixed point), then $b$ lies

• A. Outside the circle $|z-a|=3$
• B. Inside the circle $|z-a|=3$
• C. On the circumference of the circle $|z-a|=3$
• D. None of these

Answer 1

The correct option is B Inside the circle $|z-a|=3$

$|z-a|+|z-b|=3$ represents an ellipse. Now
$|a-b|<3$
$\Rightarrow |b-a|<3$
Let locus of $b\text{be}\alpha$
$\Rightarrow |\alpha -a|<3$
Which represents region inside the circle having centre at $a$ and radius $3$ units.