`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.

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

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

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

Find the locus of the midpoint of the chords of the parabola y^2=4ax .which subtend a right angle at the vertex.

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

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.

Find the length of the normal chord of a parabola y^2 = 4x , which makes an angle 45^@ with its axes.

PQ is a double ordinate of the parabola y^2=4ax Show that thelocus of its point of trisection the chord PQ is 9y^2=4ax .

Length of the focal chord of the parabola y^2=4ax at a distance p from the vertex is:

If the tangent at any point P to the parabola y^(2)=4ax meets the directrix at the point K , then the angle which KP subtends at its focus is-