Let \(\mathrm{P}(3\cos \alpha ,2\sin \alpha ),\alpha \neq 0\), be a point on the ellipse \(\frac{{x}^{2}}{9}+\frac{{y}^{…

Let \(\mathrm{P}(3\cos \alpha ,2\sin \alpha ),\alpha \neq 0\), 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 \(\left(2+\cos \alpha ,3+\frac{2}{3}\sin \alpha \right)\). Then the sum of the ordinates of all possible points R is:

[JEE Main 2026, 4 Apr (Shift 2)]