If a latus rectum of an ellipse subtends a right angle at the centre of the ellipse, then write the eccentricity of the ellipse.

If the minor axis of an ellipse subtends an equilateral triangle with vertex at one end of major axis, then write the eccentricity of the ellipse.

If the latus rectum through one focus subtends a right angle at the farther vertex of the hyperbola then its eccentricity is

If the minor axis of an ellipse subtends an angle of 60^(@) at each focus of the ellipse, then its eccentricity, is

If the latus rectum subtends a right angle at the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then find its eccentricity.

A parabola is drawn with focus at one of the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 . If the latus rectum of the ellipse and that of the parabola are same, then the eccentricity of the ellipse is (a) 1-1/(sqrt(2)) (b) 2sqrt(2)-2 (c) sqrt(2)-1 (d) none of these

If alpha and beta are the eccentric angles of the extremities of a focal chord of an ellipse, then prove that the eccentricity of the ellipse is (sinalpha+sinbeta)/("sin"(alpha+beta))

If the area of a square circumscribing an ellipse is 10 square units and maximum distance of a normal from the centre of the ellipse is 1 unit, than find the eccentricity of ellipse

If the latus rectum of an ellipse is equal to half of the minor axis, then what is its eccentricity ?

Find the length of the latus rectum of the ellipse if the eccentricity is (1)/(2) and the distance between the foci and the centre of the ellipseis 4.

A parabola is drawn whose focus is one of the foci of the ellipse x^2/a^2 + y^2/b^2 = 1 (where a>b) and whose directrix passes through the other focus and perpendicular to the major axes of the ellipse. Then the eccentricity of the ellipse for which the length of latus-rectum of the ellipse and the parabola are same is