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

Find the locus of the midpoint of chords of the parabola y^(2)=4ax that pass through the point (3a,a).

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

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

Find the locus of mid-point of chord of parabola y^(2)=4ax which touches the parabola x^(2)=4by

Find the locus of the mid-points of the chords of the parabola y^(2)=4ax which subtend a right angle at vertex of the parabola.

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.

Find the locus of middle of the chord of the parabola y^(2) = 4ax which pass through a given (p, q).

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