Explanation

(b)
Here, $a = 12,\ b = 2,\ h = - 5,\ f = - \frac{5}{2},\ g = \frac{11}{2},\ c = k\$
The given equation represents a pair of straight line, if
$abc + 2fgh - {af}^{2} - {bg}^{2} - {ch}^{2} = 0$
$\Rightarrow \ 12 \bullet 2 \bullet k + 2\left( - \frac{5}{2} \right)\left( \frac{11}{2} \right)( - 5) - 12\left( - \frac{5}{2} \right)^{2} - 2\left( \frac{11}{2} \right)^{2} - k( - 5)^{2} = 0$
$\Rightarrow \ 24k + \frac{275}{2} - \frac{150}{2} - \frac{121}{2} - 25k = 0$
$\Rightarrow \ - k + \frac{4}{2} = 0\ \Rightarrow \ k = 2$