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
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$\therefore m_{1} = m_{2} = 0$
Hence, the lines will be $y = c_{1}$ and $y = c_{2}$. Given circle is $x^{2} + y^{2} - 6x - 4y - 12 = 0$
$\therefore$ Centre (3, 2) and radius $= 5$
Here, the perpendicular drawn from centre to the lines are $CP$ and $CP^{''}$
$\therefore\ CP = \frac{2 - c_{1}}{\sqrt{1}} = \pm 5$
$\Rightarrow \ c_{1} = 7$ and $c_{1} = - 3$
Hence, the lines are
$y - 7 = 0,\ \ y + 3 = 0$
$ie,\ (y - 7)(y + 3) = 0$ or $y^{2} - 4y - 21 = 0$