Explanation

(a)
$\left| \frac{z - 5i}{z + 5i} \right| = 1\ \ \ \ \ \Rightarrow \ \ \ \ \ \ \left| \frac{x + i(y - 5)}{x + i(y + 5)} \right| = 1$
$\Rightarrow \ \ \ \ \ \left| x + i(y - 5) \right| = |x + i(y + 5)|$
$\Rightarrow \ \ \ \ \ x^{2} + 25 - 10y + y^{2} = x^{2} + y^{2} + 25 + 10y$
$\Rightarrow \ \ \ \ y = 0$