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Show that the locus of the middle points...

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

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 .

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

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