The locus of mid points of chords of the parabola `y^2 = 4ax` passing through the foot of the directrix is

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

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

Find the locus of midpoint normal chord of the parabola y^(2)=4ax

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-