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in Mathematics by (53.3k points)

The locus of the midpoints of the chords of the parabola 2y2 = 7x which are parallel to the line 3x − 2y = 0 is the line px + qy + r = 0, where |p + q + r| equals .....

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Best answer

M(x1, y1) is the midpoint of a chord so that its equation is

which is parallel to

3x -   2y = 0

 This again implies

3/2 = 7/4y1 

6y1 = 7

 The locus of point M(x1, y1) is the line 6y − 7 = 0. Hence, p = 0, q =  6, r = − 7. Thus

|p + q + r| = 1

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