Let \( P \) be a point on the ellipse \(\displaystyle \frac{x^2}{9} + \frac{y^2}{4} = 1 \). 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 \( PQ \) such that \( PR:RQ = 4:3 \) as \( P \) moves on the ellipse, is:
