The area enclosed by the closed curve \( C \) given by the differential equation \( \frac{d y}{d x}+\frac{x+a}{y-2}=0, y(1)=0 \) 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 \( R S \) is
