Let \(P\) be a point on the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}=1\). Let the line passing through \(P\) and parallel t…

Let \(P\) be a point on the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}=1\). Let the line passing through \(P\) and parallel to \(y\)-axis meet the circle \(x^2+y^2=9\) 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 :EndFragment

[JEE Main 2024, 01 Feb (Shift 2)]