Explanation

(c)
The given equation of pair of lines is ${2x}^{2} - xy - y^{2} = 0$
This can be rewritten as $(2x + y)(x - y) = 0$
So, the equation of required pair is
$\left( 2x + y + \lambda_{1} \right)\left( x - y + \lambda_{2} \right) = 0$
Where, $2x + y + \lambda_{1} = 0$ and $x - y + \lambda_{2} = 0$
These passes through (1, 0)
$\therefore\ \lambda_{1} = - 2,\ \lambda_{2} = - 1$
Thus, the required equation of pair of line is
$(2x + y - 2)(x - y - 1) = 0$
$\Rightarrow \ {2x}^{2} - xy - y^{2} - 4x + y + 2 = 0$