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Show that the locus of the middle poin...

Show that the locus of the middle points of chords of the parabola `y^(2) = 4ax` passing through the vertex is the parabola `y^(2)= 2ax` .

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The locus of the middle points of all chords of the parabola y^(2)=4ax passing through the vertex is

Prove that the locus of the middle points of all chords of the parabola y^(2)=4ax passing through the vertex is the parabola y^(2)=2ax

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