`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`

At what point on the parabola y^2=4x the normal makes equal angle with the axes?

P(alpha,alpha) is a point on the parabola y^(2)=4ax . Show that the normal chord of the parabola at P subtends a right angle at its focus.

If the normal to the parabola y^2=4a x at point t_1 cuts the parabola again at point t_2 , then prove that t_2^2 geq8.

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

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.

A normal chord of the parabola y^2=4ax subtends a right angle at the vertex, find the slope of chord.

The vertex of the parabola x^(2)-6x+4y+1=0 is

Statement 1: Normal chord drawn at the point (8, 8) of the parabola y^2=8x subtends a right angle at the vertex of the parabola. Statement 2: Every chord of the parabola y^2=4a x passing through the point (4a ,0) subtends a right angle at the vertex of the parabola. (a) Both the statements are true, and Statement-1 is the correct explanation of Statement 2. (b)Both the statements are true, and Statement-1 is not the correct explanation of Statement 2. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

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

Find the length of normal chord which subtends an angle of 90^0 at the vertex of the parabola y^2=4xdot