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

P is parabola y^2=4ax and locus of mid points of all chords of this parabola passing through the vertex of P is a parabola P'. Axis of parabola P' will be

P is parabola y^2=4ax and locus of mid points of all chords of this parabola passing through the vertex of P is a parabola P'. Axis of parabola P' will be

P is parabola y^(2)=4ax and locus of mid points of all chords of this parabola passing through the vertex of P is a parabola P' Axis of parabola P' will be

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 pointsof chords of the parabola y^2=4ax through the vertex is also a parabola.Find focus and latus rectum of the locus.

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 .

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 .

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 .