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A family of chords of the parabola y^2=4...

A family of chords of the parabola `y^2=4ax` is drawn so that their projections on a straight line inclined equally to both the axes are all of a constant length c, prove that the locus of their middle points is the curve `(y^2-4ax)(y+2a)^2+2a^2c^2=0`.

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