Explanation

(c)
Given equation can be rewritten as
$y^{2} = \frac{4k}{4}\left( x - \frac{8}{k} \right)$
The standard equation of parabola is
$Y^{2} = 4AX$, where $A = \frac{k}{4}$
$\therefore$ Equation of directrix is $X + \frac{k}{4} = 0$
$\Rightarrow x - \frac{8}{k} + \frac{k}{4} = 0$
But the given equation of directrix is $x - 1 = 0$
Since, both equations are same
$\therefore\ \frac{8}{k} - \frac{k}{4} = 1$
$\Rightarrow 32 - k^{2} = 4k\ \Rightarrow k = - 8,\ 4$