" 3.Locus of mid-points of all chords of the parabola "y^(2)=4x" which are drawn through the vertex is "

Find the locus of the middle points of all chords of the parabola y^(2) = 4ax , which are drawn through the vertex.

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 mid - points of all chords of parabola y^(2)=4x, for which all cirlces drawn taking them as diameters passes through the vertex of the parabola is a conic whose length of the smallest focal chord is equal to

The locus of mid - points of all chords of parabola y^(2)=4x, for which all cirlces drawn taking them as diameters passes through the vertex of the parabola is a conic whose length of the smallest focal chord is equal to