Let the directrix of the parabola P: y^2=8 x, cut x -axis at the point A. Let B (α, β), α>1, be a point on P such that the slope of AB is 3/5. If BC…

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