Coordinate Geometry: JEE Main 2026 Mathematics question

Let the directrix of the parabola $P: y^2=8x$, cut $x$-axis at the point A. Let $B(\alpha,\beta)$, $\alpha>1$, be a point on P such that the slope of AB is $3/5$. If BC is a focal chord of P, then six times the area of $\Delta ABC$ is :