If the eccentricity of an ellipse is zero, then show that it will be a circle.

Define eccentricity of an ellipse

The eccentricity of the ellipse

The eccentricity e of an ellipse satisfies the condition :

If the eccentricity of an ellipse is (5)/(8) and the distance between its foci is 10, then find the latusrectum of the ellipse.

If the eccentricity of an ellipse is (4)/(9) and the distance between its foci is 8 units, then find the length of the latus rectum of the ellipse.

A circle has same centre as an ellipse and passing through foci S_(1) and S_(2) of the ellipse. The two curves cut in four points. Let P be one of the points. If the Area of /_\PS_(1)S_(2) is 24 and major axis of the ellipse is 14. If the eccentricity of the ellipse is e, then the value of 7e is equal to

If the length of the eccentricity of an ellipse is (3)/(8) and the distance between the foci is 6 units, then the length of the latus rectum of the ellipse is

Let two foci of an ellipse be S_(1)(2,3) and s_(2)(2,7) and the foot of perpendicular drawn from S1 upon any tangent to the ellipse be (-1,1) . If e be the eccentricity of ellipse and R be the radius of director circle of auxiliary circle of ellipse, then find the value of (eR^(2))/(2)