Question

Which of the following option(s) is/are correct for circle represented by $\overline{z}=\overline{a}+\frac{r^2}{z-a}$

• A. Circle having centre at $-a$
• B. Circle having centre at $a$
• C. Radius of the circle $=r$
• D. Radius of the circle $=r^2$

Answer 1

Answer: (B), (C)

The correct options are
B Circle having centre at $a$
C Radius of the circle $=r$

$\overline{z}=\overline{a}+\frac{r^2}{z-a}$
$\Rightarrow \overline{z}-\overline{a}=\frac{r^2}{z-a}$ $\Rightarrow (z-a)\overline{(z-a)}=r^2$
$\Rightarrow |z-a{|}^2=r^2$
$\Rightarrow |z-a|=r$
Hence, locus of $z$ is circle having centre at $a$ and radius $r$. units