The area enclosed by the closed curve \( C \) given by the differential equation \( \dfrac{dy}{dx}+\dfrac{x+a}{y-a}=0,\ y(1)=0 \) is \( 4\pi \).
Let \( P \) and \( Q \) be the points of interaction of the curve \( C \) and the y-axis. If normal 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 :
