The area enclosed by the closed curve $$C$$ given by the differential equation $$\frac{dy}{dx} + \frac{x+a}{y-2} = 0$$, $$y(1) = 0$$ is $$4\pi$$. Let $$P$$ and $$Q$$ be the points of intersection of the curve $$C$$ and the $$y$$-axis. If normals at $$P$$ and $$Q$$ on the curve $$C$$ intersect $$x$$-axis at points $$R$$ and $$S$$ respectively, then the length of the line segment $$RS$$ is

A

$$2\sqrt{3}$$

B

$$\frac{2\sqrt{3}}{3}$$

C

2

D

$$\frac{4\sqrt{3}}{3}$$