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If from the vertex of the parabola y^(2)...

If from the vertex of the parabola `y^(2)=4ax`, a pair of chords be drawn at right angles to one another and with these chords as adjacent sides, a rectangle be drawn, prove that the locus of the vertex of the rectangle, farthest from origin, is the parabola `y^(2)=4a(x-8a)`.

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