Explanation

(c)
The pair of asymptotes and second degree curve differ by a constant.
$\therefore\$Pair of asymptotes is
$2x^{2} + 5xy + 2y^{2} - 11x - 7y + \lambda = 0$ …(i)
Hence, Eq. (i) represents a pair of straight lines.
$\therefore\ \mathrm{\Delta} = 0$
$\Rightarrow \ \ 2 \times 2 \times \lambda + 2 \times - \frac{7}{2} \times - \frac{11}{2} \times \frac{5}{2} - 2 \times \left( - \frac{7}{2} \right)^{2} - 2 \times \left( - \frac{11}{2} \right)^{2} - \lambda \times \left( \frac{5}{2} \right)^{2} = 0$
$\Rightarrow \ \ \lambda = 5$
From Eq.(i), pair of asymptotes is
$2x^{2} + 5xy + 2y^{2} - 11x - 7y + 5 = 0\$