Find the locus of the centre of the circle passing through the vertex and the mid-points of perpendicular chords from the vertex of the parabola `y^2 =4ax` .

IF (a,b) is the mid point of chord passing through the vertex of the parabola y^2=4x , then

IF (a,b) is the mid point of chord passing through the vertex of the parabola y^2=4x , then

Prove that the locus of the centre of the circle, which passes through the vertex of the parabola y^(2)=4ax& through its intersection with a normal chord is 2y^(2)=ax-a^(2)

Show that the locus of the mid point of chords of a parabola passing through the vertex is a parabola

In the parabola y^(2)= 4ax the length of the chord passing through the vertex and inclined to the axis at pi//4

If the parabola y^(2) = 4ax passes through the point (4, 1), then the distance of its focus the vertex of the parabola is

If the parabola y^(2) = 4ax passes through the point (4, 1), then the distance of its focus the vertex of the parabola is

The locus of foot of the perpendiculars drawn from the vertex on a variable tangent to the parabola y^2 = 4ax is