The length of tangent between the point of contact and the point where it meets the directrix subtends right angle at corresponding 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.

Any point P of an ellipse is joined to the extremities of the major axis; prove that the portion of a directrix intercepted by them subtends a right angle at the corresponding focus.

Prove that the normal chord to a parabola at the point whose ordinate is equal to the abscissa subtends a right angle at the focus.

The actue angle between the tangent at those points on the curve y=(x+1)(x-3) where it meets the X-axes is

The tangent at the point alpha on a standard ellipse meets the auxiliary circle in two points which subtends a right angle at the centre. Show that the eccentricity of the ellipse is (1+ sin^2aplha)^-1/2 .

Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre.

Let P be any point on any directrix of an ellipse. Then the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at (a)some point on the major axis depending upon the position of point Pdot (b)the midpoint of the line segment joining the center to the corresponding focus (c)the corresponding focus (d)none of these

Show that the locus of the point of intersection of the tangents at the extremities of any focal chord of an ellipse is the directrix corresponding to the focus.

The angle made by the tangent and the radius made at the point of contact is