Coordinate Geometry: JEE Main 2026 Mathematics question

Let $P(3\cos\alpha, 2\sin\alpha)$, $\alpha\neq0$, be a point on the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$, $Q$ be a point on the circle $x^2+y^2-14x-14y+82=0$ and $R$ be a point on the line $x+y=5$ such that the centroid of the triangle $PQR$ is $\left(2+\cos\alpha,\,3+\frac23\sin\alpha\right)$. Then the sum of the ordinates of all possible points $R$ is: