Explanation

(d)
Condition for line $lx + my + n = 0$ is normal to the ellipse is
$\frac{a^{2}}{l^{2}} + \frac{b^{2}}{m^{2}} = \frac{\left( a^{2} - b^{2} \right)^{2}}{n^{2}}\$
Here, $l = 2,\ m = - \frac{8}{3}\ \lambda,n = 3,\ a^{2} = 1,\ b^{2} = 4\$
$\therefore\ \frac{1}{2^{2}} + \frac{4}{\left( - \frac{8}{3}\lambda \right)^{2}} = \frac{(1 - 4)^{2}}{(3)^{2}}$
$\Rightarrow \frac{1}{4} + \frac{36}{64\lambda^{2}} = 1$
$\Rightarrow \ \lambda^{2} = \frac{9 \times 4}{16 \times 3},\ \lambda = \pm \frac{\sqrt{3}}{2}$