Explanation

(a)
Let the lines are $y = m_{1}x + c_{1}$ and $y = m_{2}x + c_{2}$
Since, pair of straight lines are parallel to $x$-axis
$\therefore m_{1} = m_{2} = 0$
and the lines will be $y = c_{1}$ and $y = c_{2}$
Given circle is $x^{2} + y^{2} - 6x - 4y - 12 = 0$
Centre (3, 2) and radius $= 5$
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Here, the perpendicular drown from centre to the lines are $CP$ and $CP''$
$\therefore CP = \frac{2 - c_{1}}{\sqrt{1}} = \pm 5$
$\Rightarrow 2 - c_{1} = \pm 5$
$\Rightarrow \ \ c_{1} = 7\ and\ c_{1} = - 3$
Hence, the lines are
$y - 7 = 0,\ y + 3 = 0,\ ie,\ (y - 7)(y + 3) = 0$
$\therefore\$Pair of straight lines is $y^{2} - 4y - 21 = 0$