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Ellipse and its Elements

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The ratio of ordinates of a point on ellipse and its corresponding point on auxiliary circle is (2sqrt(2))/(3) then its eccentricity is

If the ratio of the ordinate of a point on ellipse and its corresponding point on auxiliary circle is (2sqrt(2))/(3) then its eccentricity is

If distance between foci of an ellipse equals its latus-rectrum , then its eccentricity is

The ratio of the area enclosed by the locus of the midpoint of PS and area of the ellipse is (P-be any point on the ellipse and S, its focus)

If a triangle is inscribed in a n ellipse and two of its sides are parallel to the given straight lines,then prove that the third side touches the fixed ellipse.

The distance between the foci of an ellipse is 10 and its latus rectum is 15, find its equation referred to its axes as axes of coordinates.

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