Chord of parabola and line interactionMedium

Area of Parabolic Focal Chord Triangle

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 $\triangle ABC$ is:

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