Explanation

(c)
Equating of the planes through $y = mx,\ \mathcal{z} = c$ and $y = - mx,\ \mathcal{z} = - c$ are respectively,
$(y - mx) + \lambda_{1}\left( \mathcal{z} - c \right) = 0$ (i)
and $(y + mx) + \lambda_{2}\left( \mathcal{z} + c \right) = 0$ (ii)
It meets at $x$-axis, i.e., $y = 0 = \mathcal{z}$
$\therefore\ \lambda_{2} = \lambda_{1}$
From (i) and (ii), $\frac{y - mx}{\mathcal{z} - c} = \frac{y + mx}{\mathcal{z} + c}$
$\therefore cy = m\mathcal{z}x$