If \(A\) and \(B\) are the points of intersection of the circle \(x^2+y^2-8 x=0\) and the hyperbola \(\frac{x^2}{9}-\fra…

If \(A\) and \(B\) are the points of intersection of the circle \(x^2+y^2-8 x=0\) and the hyperbola \(\frac{x^2}{9}-\frac{y^2}{4}=1\) and a point \(P\) moves on the line \(2 x-3 y+4=0\), then the centroid of \(\triangle P A B\) lies on the line :

[JEE Main 2025, 28 Jan (Shift 2)]