Explanation

(a)
To make the given curves $x^{2} + y^{2} = 4\ and\ x + y = a$ homogeneous.
$x^{2} + y^{2} - 4\left( \frac{x + y}{a} \right)^{2} = 0$
$\Rightarrow \ a^{2}\left( x^{2} + y^{2} \right) - 4\left( x^{2} + y^{2} + 2xy \right) = 0$
$\Rightarrow \ x^{2}\left( a^{2} - 4 \right) + y^{2}\left( a^{2} - 4 \right) - 8xy = 0$
Since, this is a perpendicular pair of straight lines.
$\therefore\ a^{2} - 4 + a^{2} - 4 = 0$
$\Rightarrow \ a^{2} = 4\ \Rightarrow \ a = \pm 2$
Hence, required set of $a$ is $\{ - 2,\ 2\}$.