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 point on the parabola y ^(2) = 36x whose ordinate is three times the abscissa, is

The normal chord of y^(2)=4ax at a point where abscissa is equal to ordinate subtends at the focus an angle theta

Equal chords of a circle subtend equal angles at the centre.

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.

The normal meet the parabola y^(2)=4ax at that point where the abscissa of the point is equal to the ordinate of the point is

The co-ordinates of a point on the parabola y^(2)=8x whose ordinate is twice of abscissa, is :