If the segment intercepted by the parabola `y^2=4a x` with the line `l x+m y+n=0` subtends a right angle at the vertex, then

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.

Statement 1: If the straight line x=8 meets the parabola y^2=8x at Pa n dQ , then P Q substends a right angle at the origin. Statement 2: Double ordinate equal to twice of latus rectum of a parabola subtends a right angle at the vertex.

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

A normal chord of the parabola y^2=4ax subtends a right angle at the vertex if its slope is

The radius of the circle whose centre is (-4,0) and which cuts the parabola y^(2)=8x at A and B such that the common chord AB subtends a right angle at the vertex of the parabola is equal to

The area bounded by the parabola y = x^(2) and the line y = 2x is

A is a point on the parabola y^2=4a x . The normal at A cuts the parabola again at point Bdot If A B subtends a right angle at the vertex of the parabola, find the slope of A Bdot

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

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

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