The area enclosed by the closed curve C given by the differential equation (d y)/(d x)+(x+a)/(y-2)=0, y(1)=0 is 4 π. Let P and Q be the points of…

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