Circles are described on the chords of the parabola `y^(2)=4ax` drawn though the vertex.The locus of the centres of circle

The normal chord of the parabola y^(2)=4ax subtends a right angle at the vertex.Then the length of chord is

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

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

A chord of parabola y^(2)=4ax subtends a right angle at the vertex The tangents at the extremities of chord intersect on

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

A variable circle is described to pass through the point (1,0) and tangent to the curve y=tan(tan^(-1)x). The locus of the centre of the circle is a parabola whose