Explanation

(a)
Let the equation $y = mx + c$ be the common tangents so the curve $y^{2} = 8x$ and $x^{2} + y^{2} = 2$
Then, $c = \frac{2}{m}$ and $c^{2} = 2(1 + m^{2})$
If $m^{2} = t$, then
$\frac{4}{t} = 2(1 + t) \Rightarrow t^{2} + t - 2 = 0$
$\Rightarrow (t + 2)(t - 1) = 0 \Rightarrow t = 1,\ - 2$
Thus, $m = \pm 1$ $(\because t \neq - 2)$
Hence, tangents are $y = x + c$ and $y = - x + c$ which are perpendicular to each other