Explanation

(c)
Let the equation of tangent parallel to $x + 2y + 3 = 0$ be $x + 2y + \lambda = 0$
Condition for tangency
$\left( - \frac{\lambda}{2} \right)^{2} = 4\left( 1 + \frac{1}{4} \right)\ \ \ \ \ \lbrack\because\ \ c^{2} = a^{2}(1 + m^{2})\rbrack$
$\Rightarrow \ \ \ \lambda^{2} = 20\ \ \ \Rightarrow \ \ \ \ \lambda = \pm 2\sqrt{5}$
$\therefore$Required equation of tangent is
$x + 2y = \pm 2\sqrt{5}$