Show that the locus of a point that divides a chord of slope 2 of the parabola `y^2=4x` internally in the ratio `1:2` is parabola. Find the vertex of this parabola.

Find the vertex of the parabola x^2=2(2x+y)

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

The vertex of the parabola y^2 = 4x + 4y is

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

The vertex of the parabola y^2 + 4x = 0 is

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 the point of intersection of perependicular tangent of the parabola y^(2) =4ax is

The vertex of the parabola x^(2)=8y-1 is :

Prove that the chord y-xsqrt(2)+4asqrt(2)=0 is a normal chord of the parabola y^2=4a x . Also find the point on the parabola when the given chord is normal to the parabola.

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