An ellipse inscribed in a semi-circle touches the circular arc at two distinct points and also touches the bounding diameter. Its major axis is parallel to the bounding diameter. When the ellipse has the maximum possible area, its eccentricity is-
Consider an ellipse, whose center is at the origin and its major axis is along the -axis. If its eccentricity is and the distance between its foci is , then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is:
In an ellipse, its foci and the ends of its major axis are equally spaced. If the length of its semi-minor axis is then the length of its semi-major axis is
If the length of the latus rectum of an ellipse is units and the distance between a focus and its nearest vertex on the major axis is units, then its eccentricity is
If is the semi-minor axis of an ellipse, and are its focii and the angle between and is a right angle, then the square of the eccentricity of the ellipse is
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 then the length of its latus rectum is:
An ellipse passes through the foci of the hyperbola, and its major and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is then which of the following points does not lie on the ellipse?
Let and be the foci of an ellipse and be any one of the extremities of its minor axis. If is a right angled triangle with right angle at and area , then the length of a latus rectum of the ellipse is :
