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 `

Similar Questions

Explore conceptually related problems

The locus of the middle points of the focal chords of the parabola, y^2=4x is:

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

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

Find the locus of the midpoint of normal chord of parabola y^2=4a xdot

Find the locus of the middle points of the chords of the parabola y^2=4a x which subtend a right angle at the vertex of the parabola.

The locus of middle points of a family of focal chord of the parabola y^(2) =4 ax is-

Find the locus of the midpoint of the chords of the parabola y^2=4ax .which subtend a right angle at the vertex.

Length of the shortest normal chord of the parabola y^2=4ax is

Length of the focal chord of the parabola y^2=4ax at a distance p from the vertex is:

Show that the product of the ordinates of the ends of a focal chord of the parabola y^(2) = 4ax is constant .