Find The Locus Of The Point Of Intersection Of The Tangents To The Ellipse , If The Difference Of The Eccentric Angle Of Their Points Of Contact Is 2α.

If  is a tangent to the ellipse , then find out the eccentric angle of the point of tangency.

For what value of λ dose the line y = x + λ touches the ellipse 9x² + 16y² = 144.

Find the equations of the tangents to the ellipse 3x² + 4y² = 12 which perpendicular to the line y + 2x = 4.

Find the equation of pair of tangents drawn from the point (1, 2) and (2, 1) to the ellipse .

A tangent to the circle x² + y² = 5 at the point (–2, 1) intersect the ellipse  at the point A, B. If tangents to the ellipse at the point A and B intersect at point C. Find the coordinate of points C.

If the line 3y = 3x + 1 is a normal to the ellipse , then find out the length of the minor axis of the ellipse.

If SK be the perpendicular from the focus S on the tangent at any point P on the ellipse , then locus of K is 

The tangent and normal to the ellipse x² + 4y² = 4 at a point P(θ) in second quadrant, meet the major axis in Q and R respectively. If QR = 2, then cos θ is equal to

If latus rectum of the ellipse  is equal to

In an ellipse, the distance between its foci is 6 and minor axis 8. The eccentricity of the ellipse is