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Chord of a parabola making a triangle with the focus whose centroid is given: length of the chord

The same question, asked 2 times: 8 Apr 2023*, 28 Jan 2026 S2. Every wording below, oldest first.

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  1. Question 1

    8 Apr 2023

    63
    Let RR be the focus of the parabola y2=20xy^{2}= 20x and the line y=mx+cy = mx + c intersect the parabola at two points PP and QQ. Let the point G(10,10)G(10,10) be the centroid of the triangle PQRPQR. If c−m=6c - m = 6, then (PQ)2(PQ)^{2} is

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  2. Question 2

    28 Jan 2026 S2

    53
    Let A be the focus of the parabola y2=8xy^{2}= 8x. Let the line y=mx+cy = mx + c intersect the parabola at two distinct points B and C . If the centroid of the triangle ABCABC is (73,43)\left( \frac{7}{3},\frac{4}{3} \right), then (BC)2(BC)^{2} is equal to :

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