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Show that the locus of the mid-points of...

Show that the locus of the mid-points of all chords passing through the vertices of the parabola `y^(2)`=4ax is the parabola `y^(2)=2ax`.

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Show that the locus of the mid point of chords of a parabola passing through the vertex is a parabola

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

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 .

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 midpoints of all chords of the parabola y^(2)=4ax through its vertex is another parabola with directix