Prove that the tangent at one extremity of the focal chord of a parabola is parallel to the normal at the other extremity.

Show that the tangents at the extremities of any focal chord of a parabola intersect at right angles at the directrix.

Prove that the tangents at the extremities of any chord make equal angles with the chord.

Prove that the circle described on the focal chord of parabola as a diameter touches the directrix

If ((1)/(2),2) is one extermity of a focalchord of the parabola y^(2)=8x. Find the co-ordinates of the other extremity.

Prove that the length of a focal chord of a parabola varies inversely as the square of its distance from the vertex.

. Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.

Statement-1: The tangents at the extremities of a focal chord of the parabola y^(2)=4ax intersect on the line x + a = 0. Statement-2: The locus of the point of intersection of perpendicular tangents to the parabola is its directrix

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 .

Angle between tangents drawn at ends of focal chord of parabola y^(2) = 4ax is

Prove that the line joining the orthocentre to the centroid of a triangle formed by the focal chord of a parabola and tangents drawn at its extremities is parallel to the axis of the parabola.