Conic Sections · Parabola parametric chord and centroid

Let

A

be the focus of the parabola

y^2 = 8x

. Let the line

y = mx + c

intersect the parabola at two distinct points

B

and

C

. If the centroid of the triangle

ABC

\left(\dfrac73, \dfrac43\right)

, then

(BC)^2

is equal to :

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