Explanation

(b)
Directrix of $y^{2} = 4(x + 1)$ is $x = - 2$. Any point on $x = - 2$ is $( - 2,\ k)$
Now mirror image $(x,\ y)$ of $( - 2,\ k)$ in the line $x + 2y = 3$ is given by
$\frac{x + 2}{1} = \frac{y - k}{2} = - 2\left( \frac{- 2 + 2k - 3}{5} \right)$
$\Rightarrow x = \frac{10 - 4k}{5} - 2$
$\Rightarrow x = - \frac{4k}{5}$ …(i)
And $y = \frac{20 - 8k}{5} + k$
$\Rightarrow y = \frac{20 - 3k}{5}$ …(ii)
From Eqs. (i) and (ii), we get
$y = 4 + \frac{3}{5}\left( \frac{5x}{4} \right)$
$\Rightarrow y = 4 + \frac{3x}{4}$
$\Rightarrow 4y = 16 + 3x$ is the equation of the mirror image of the directrix