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 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:

Differential Equations: JEE Main 2023 Mathematics question

JEE Main 2023 · 1 Feb, Morning shift · Q3633

JEE Main 20231 Feb, Morning shiftMathematicsMediumDifferential Equations163× since 2002

The area enclosed by the closed curve

\mathrm{C}

given by the differential equation

\frac{d y}{d x}+\frac{x+a}{y-2}=0, y(1)=0

4 \pi

. Let

P

and

Q

be the points of intersection of the curve

\mathrm{C}

and the

y

-axis. If normals at

P

and

Q

on the curve

\mathrm{C}

intersect

x

-axis at points

R

and

S

respectively, then the length of the line segment

R S

is :