Explanation

(c)
Given, $\overline{z} = \overline{a} + \frac{r^{2}}{z - a}\ ,\ \ r > 0$
$\Rightarrow \ \ \overline{z}(z - a) = \overline{a}(z - a) + r^{2}$
$\Rightarrow \ \ \ \ \ z\overline{z} - a\overline{z} - \overline{a}z + a\overline{a} + r^{2} = 0$
This represents the equation of a circle