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.

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

Tangent OF Ellipse

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

If the portion of the line ax - by - 1 = 0 , intercepted between the lines ax + y + 1 = 0 and x + by = 0 subtends a right angle at the origin , then find value of 4a +b^2 + (b+1)^2 .

For the curve xy=c, prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.

At some point P on the ellipse the segments ss' subtends a right angle then its eccentricity