JEE Main 2026 · 4 Apr · Shift 2, Mathematics question 10

Let $P(3\cos\alpha,2\sin\alpha)$, $\alpha\ne0$, be a point on the ellipse $\dfrac{x^2}9+\dfrac{y^2}4=1$, 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 $\left(2+\cos\alpha,\ 3+\dfrac23\sin\alpha\right)$. Then the sum of the ordinates of all possible points R is: