If the tangent to the parabola y² = x at a point ($$\alpha $$, $$\beta $$), ($$\beta $$ > 0) is also a tangent to the ellipse, x² + 2y² = 1, then $$\alpha $$ is equal to :

In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is 10 and one of the foci is at (0,5$$\sqrt 3$$), then the length of its latus rectum is :

If the tangents on the ellipse 4x² + y² = 8 at the points (1, 2) and (a, b) are perpendicular to each other, then a² is equal to :

Let S and S' be the foci of an ellipse and B be any one of the extremities of its minor axis. If $$\Delta $$S'BS is a right angled triangle with right angle at B and area ($$\Delta $$S'BS) = 8 sq. units, then the length of a latus rectum of the ellipse is :