Explanation

(c)
Centre of circle is (0, 0)
Equation of tangent which is parallel to $x + 2y + 3 = 0$ is
$x + 2y + \lambda = 0$ …(i)
As we know perpendicular distance from centre (0, 0) to $x + 2y + \lambda = 0$ should be equal to radius
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$\therefore\ \frac{0 + 2 \times 0 + \lambda}{\sqrt{1^{2} + 2^{2}}} = \pm 2$
$\Rightarrow \ \lambda = \pm 2\sqrt{5}$
On putting the value of $\lambda$ in Eq. (i), we get
$x + 2y = \pm 2\sqrt{5}$
Which represents the required equation of tangents