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Prove that the locus of the middle point...

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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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

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 .

The locus of the middle points of normal chords of the parabola y^2 = 4ax is-

The locus of the middle points of normal chords of the parabola y^2 = 4ax is-

The locus of the middle points of normal chords of the parabola y^2 = 4ax is-

The locus of middle points of normal chords of the parabola y^(2) = 4ax is

The locus of the middle points of normal chords of the parabola y^(2)=4ax is-