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

The length of the chord of the parabola x^(2) = 4y passing through the vertex and having slope cot alpha is

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)

The length of the chord of the parabola x^(2) = 4 y passing through the vertex and having slops cot alpha is

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

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

Length of the chord of the parabola y^(2)=4ax passing through the vertex and making an angle theta (0< theta < pi ) with the axis of the parabola