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

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

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

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

If the tangents and normals at the extremities of a focal chord of a parabola intersect at (x_1,y_1) and (x_2,y_2), respectively, then (a) x_1=y_2 (b) x_1=y_1 (c) y_1=y_2 (d) x_2=y_1

Show that the tangents at the extremities of the latus rectum of an ellipse intersect on the corresponding directrix.

Circles are described on any focal chords of a parabola as diameters touches its directrix

The locus of the point of intersection of tangents drawn at the extremities of a focal chord to the parabola y^2=4ax is the curve

If alpha and beta are the eccentric angles of the extremities of a focal chord of an ellipse, then prove that the eccentricity of the ellipse is (sinalpha+sinbeta)/("sin"(alpha+beta))

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