Explanation

(c)
On comparing given equation with standard equation, we get
$a = 1,\ b = - 1,\ c = - 2,\ h = 0,\ g = - 1/2\ ,f = \lambda/2$
Given equation represent a pair of straight line,
$\therefore abc + 2\ fgh - {af}^{2} - {bg}^{2} - {ch}^{2} = 0$
$\Rightarrow \ 2 + 0 - \frac{\lambda^{2}}{4} + \frac{1}{4} = 0$
$\Rightarrow \ \frac{\lambda^{2}}{4} = \frac{9}{4}\ \ \ \Rightarrow \ \ \lambda = \pm 3$