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)…

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

[JEE Main 2023, 1 Feb (Shift 1)]