Explanation

(c)
On comparing the given line with
${ax}^{2} + 2hxy + {by}^{2} + 2gx + 2fy + c = 0$
we get,
$a = \lambda,\ \ h = - 5,\ \ b = 12,\ g = \frac{5}{2},\ f = - 8,\ c = - 3$
It represents a pair of line, if
$\lambda \times 12 \times ( - 3) + 2( - 8)\left( \frac{5}{2} \right)( - 5) - \lambda( - 8)^{2} - 12\left( \frac{5}{2} \right)^{2} + 3( - 5)^{2} = 0$
$\Rightarrow \ \ - 36\lambda + 200 - 64\lambda - 75 + 75 = 0$
$\Rightarrow \ 100\lambda = 200\ \Rightarrow \ \lambda = 2$