Prove that the portion of the tangent intercepted,between the point of contact and the directrix of the parabola `y^(2)= 4ax` subtends a right angle at its focus.

Foot of the directrix of the parabola y^(2) = 4ax is the point

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

The point of contact of 2x-y+2 =0 to the parabola y^(2)=4ax is

Statement 1: In the parabola y^2=4a x , the circle drawn the taking the focal radii as diameter touches the y-axis. Statement 2: The portion of the tangent intercepted between the point of contact and directrix subtends an angle of 90^0 at focus.

Prove that the portion of the tangent to an ellipse intercepted between the ellipse and the directrix subtends a right angle at the corresponding focus.

Show that the length of the tangent to the parabola y^2 = 4ax intercepted between its point of contact and the axis of the parabola is bisected by the tangent at the vertex.

If the normal chord drawn at the point t to the parabola y^(2) = 4ax subtends a right angle at the focus, then show that ,t = pmsqrt2

If a normal chord at a point on the parabola y^(2)=4ax subtends a right angle at the vertex, then t equals

prove that the locus of the point of intersection of the tangents at the extremities of any chord of the parabola y^2 = 4ax which subtends a right angle at the vertes is x+4a=0 .

If the chord joining the points t_1 and t_2 on the parabola y^2 = 4ax subtends a right angle at its vertex then t_1t_2=