If the distance between two latus rectum of a ellipse is `10` unit and length of major axis `12`unit then find its eccentricity.

Show that the tangents at the ends of latus rectum of an ellipse intersect on the major axis.

If the distance between the foci of an ellipse is equal to the length of the latus rectum, then its eccentricity is _

Let the length of latus rectum of an ellipse with its major axis along x-axis and center at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of the minor axis , then which of the following points lies on it: (a) (4sqrt2, 2sqrt2) (b) (4sqrt3, 2sqrt2) (c) (4sqrt3, 2sqrt3) (d) (4sqrt2, 2sqrt3)

If the latus rectum of a hyperbola is equal to half of its transverse axis, then its eccentricity is -

The length of the latus rectum of an ellipse is 8 unit and that of the mojor axis , which lies along the x -axis, is 18 unit. Find its equation in the standard form . Determine the coordinates of the foci and the eqations of its directrices .

The latus rectum of an ellipse is equal to one-half of its minor axis. The eccentricity of the ellipse is

The distance between two directrices of a rectangular hyperbola is 10 units. Find the distance between its foci.

If the length of latus rectum of a rectangular hyperbola is 6 unit, find its equation.

The length of latus rectum of an ellipse is equal to the length of its semi-minor axis . The ratio of lengths of its minor axis and major axis is _

In each of the Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse. (x^(2))/(4)+(y^(2))/(25)=1