Explanation

(d)
Given line is
$x^{2} + 2xy - {35y}^{2} - 4x + 44y - 12 = 0$
Here, $a = 1,\ b = - 35,\ c = - 12,\ h = 1,\ f = 22$
$\therefore Point\ of\ intersection = \left( \frac{22 - 70}{- 35 - 1},\frac{- 2 - 22}{- 35 - 1} \right) = \left( \frac{4}{3},\frac{2}{3} \right)$
If the lines are concurrent. The point $\left( \frac{4}{3},\frac{2}{3} \right)$ will be on the line $5x + \lambda y - 8 = 0$
$\therefore 5\left( \frac{4}{3} \right) + \lambda\left( \frac{2}{3} \right) - 8 = 0$
$\Rightarrow \ \frac{2}{3}\lambda = 8 - \frac{20}{3} = \frac{4}{3} \Rightarrow \lambda = 2$