Let P be a point on the ellipse (x²)/9+(y²)/4=1. Let the line passing through P and parallel to y -axis meet the circle x²+y²=9 at point Q such that P and Q are on the same side of the x -axis. Then, the eccentricity of the locus of the point R on P Q such that P R: R Q=4: 3 as P moves on the ellipse, is:

Coordinate Geometry: JEE Main 2024 Mathematics question

JEE Main 2024 · 1 Feb, Evening shift · Q3726

JEE Main 20241 Feb, Evening shiftMathematicsHardCoordinate Geometry478× since 2002

Let

\mathrm{P}

be a point on the ellipse

\frac{x^2}{9}+\frac{y^2}{4}=1

. Let the line passing through

\mathrm{P}

and parallel to

y

-axis meet the circle

x^2+y^2=9

at point

\mathrm{Q}

such that

\mathrm{P}

and

\mathrm{Q}

are on the same side of the

x

-axis. Then, the eccentricity of the locus of the point

R

P Q

such that

P R: R Q=4: 3

P

moves on the ellipse, is :

JEE Main 2024 · 1 Feb, Evening shift · Q3726

JEE Main 20241 Feb, Evening shiftMathematicsHardCoordinate Geometry478× since 2002

Let

\mathrm{P}

be a point on the ellipse

\frac{x^2}{9}+\frac{y^2}{4}=1

. Let the line passing through

\mathrm{P}

and parallel to

y

-axis meet the circle

x^2+y^2=9

at point

\mathrm{Q}

such that

\mathrm{P}

and

\mathrm{Q}

are on the same side of the

x

-axis. Then, the eccentricity of the locus of the point

R

P Q

such that

P R: R Q=4: 3

P

moves on the ellipse, is :