Explanation

(b)
Here, $a = a,\ h = 0,\ b = - 1,\ f = - \frac{1}{2},\ g = 2,\ c = 0$
Given equation represent a pair of straight line.
$Then,\ \left| \begin{matrix}
a & 0 & 2 \\
0 & - 1 & - 1/2 \\
2 & - 1/2 & 0
\end{matrix} \right| = 0$
$\Rightarrow \ a\left\lbrack 0 - \left( \frac{1}{4} \right) \right\rbrack - 0 + 2\lbrack 2\rbrack = 0\ \ \Rightarrow \ a = 16$