Explanation

(b)
Given equation of an ellipse can be rewritten as
$\frac{(x - 1)^{2}}{1/8} + \frac{(y + 1)^{2}}{1/6} = 1$
Here, $b > a$
Now, $e = \sqrt{1 - \frac{1/8}{1/6}} = \frac{1}{2}$
$\therefore$ Directrix,$\ y + 1 = \pm \left( \frac{\sqrt{1/6}}{1/2} \right)\ \ \ \left\lbrack \because y = \pm \frac{b}{e} \right\rbrack$
$\Rightarrow \ y + 1 = \pm \frac{2}{\sqrt{6}}\ \Rightarrow \ 3y + 3 = \pm \sqrt{6}$