Question

Identify the locus of z if $\overline{z}=\overline{a}+\frac{r^2}{z-a}>0$.

• A. $|z-\overline{a}|=r$
• B. $|z-\overline{a}|=2r$
• C. $|z-a|=2r$
• D. $|z-a|=r$

Answer 1

The correct option is D $|z-a|=r$

$\overline{z}=\overline{a}+\frac{r^2}{z-a}$
or
$\overline{z}-\overline{a}=\frac{r^2}{z-a}$
or $(z-a)(\overline{z}-\overline{a})=r^2$
or ${|z-a|}^2=r^2$
or $|z-a|=r$
Hence, locus of z is circle having center a and radius r.
Ans: D