If the minor axis of an ellipse is equal to the distance between its foci, prove that its eccentricity is `1/sqrt(2)`.

Consider an ellipse x^2/a^2+y^2/b^2=1 Let a hyperbola is having its vertices at the extremities of minor axis of an ellipse and length of major axis of an ellipse is equal to the distance between the foci of hyperbola. Let e_1 and e_2 be the eccentricities of an ellipse and hyperbola respectively. Again let A be the area of the quadrilateral formed by joining all the foci and A, be the area of the quadrilateral formed by all the directrices. The relation between e_1 and e_2 is given by

In an ellipse, the distances between its foci is 6 and minor axis is 8 . Then its eccentricity is

If the focal distance of the one end of the minor axis of standard ellipse is k and distance between its foci is 2h(kgth) , then find its equation.

Find the equation of the ellipse whose centre is at origin, the distance between foci is 2 and eccentricity is (1)/(sqrt(2)) .

Find the equation of the ellipse whose centre is at (0, 2) and major axis along the axis of y and whose minor axis is equal to the distance between the foci and whose latus rectum is 2.

If the distance between the foci of an ellipse is equal to length of minor axis, then its eccentricity is

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

Find the equation to the ellipse with axes as the axes of coordinates. the minor axis is equal to the distance between the foci, and the latus rectum is 10.

If the major axis of an ellipse is three times the minor axis, then its eccentricity is equal to a. 1/3 b. 1/(sqrt(3)) c. 1/(sqrt(2)) d. (2sqrt(2))/3 e. 3/(3sqrt(2))

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