Explanation

(a)
Given, $\alpha$ be the distance between lines
$x - y + 2 = 0\ and\ x - y - 2 = 0$
$\therefore\ \alpha = \frac{|2 + 2|}{\sqrt{1 + 1}} = \frac{|4|}{\sqrt{2}} = 2\sqrt{2}$
and $\beta$ be the distance between the lines
$4x - 3y - 5 = 0\ and\ 4x - 3y + \frac{1}{2} = 0$
$\therefore\ \beta = \frac{\left| 5 + \frac{1}{2} \right|}{\sqrt{(4)^{2} + (3)^{2}}} = \frac{|11|}{2\sqrt{25}} = \frac{11}{10}$
$Now,\frac{\alpha}{\beta} = \frac{2\sqrt{2}}{11/10} = \frac{20\sqrt{2}}{11}$
$\Rightarrow 20\sqrt{2}\beta = 11\alpha$