Let \(A\) be the focus of the parabola \(y^2=8 x\). Let the line \(y=m x+c\) intersect the parabola at two distinct poin…

Let \(A\) be the focus of the parabola \(y^2=8 x\). Let the line \(y=m x+c\) intersect the parabola at two distinct points \(B\) and \(C\) . If the centroid of the \(\triangle A B C\) is \(\left(\frac{7}{3}, \frac{4}{3}\right)\), then \((B C)^2\) is equal to:

[JEE Main 2026, 28 Jan (Shift 2)]