Let P be a point on the ellipse x^2/9+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…

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 $\displaystyle x^2+y^2=9$ at point Q such that P and Q are on the same side of the $\displaystyle x$-axis. Then, the eccentricity of the locus of the point $\displaystyle R$ on $\displaystyle P Q$ such that $\displaystyle P R$ : $\displaystyle R Q=4: 3$ as $\displaystyle P$ moves on the ellipse, is: