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

A circle has the same center as an ellipse and passes through the foci F_1a n dF_2 of the ellipse, such that the two cuves intersect at four points. Let P be any one of their point of intersection. If the major axis of the ellipse is 17 and the area of triangle P F_1F_2 is 30, then the distance between the foci is (a)13 (b) 10 (c) 11 (d) none of these

A circle concentric with the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and passes through the foci F_(1) and F_(2) of the ellipse.Two curves intersect at fur points.Let P be any point of intersection.If the major axis of the ellipse is 15 and the area of triangle PF_(1)F_(2) is 26, then find the valueof 4a^(2)-4b^(2).

An ellipse passing through origin has its foci at (5,12) and (24,7) .Then its eccentricity is

An ellipse passing through origin has its foci at (5,12) and (24,7) .Then its eccentricity is

An ellipse has foci (4, 2), (2, 2) and it passes through the point P (2, 4). The eccentricity of the ellipse is

The line joining the foci F and F' of an ellipse subtend a right angle at the positive end B of the minor axis.If e is the eccentricity of the ellipse then the value of 2e^(2)+1 is equal to

Let x+2=0 is a tangent to an ellipse whose foci are (1,3) and (4,7) .If e is the eccentricity of the ellipse then e^(2)+(266)/(97) is equal to

Let S=(3,4) and S'=(9,12) be two foci of an ellipse.If the coordinates of the foot of the perpendicular from focus S to a tangent of the ellipse is (1,-4) then the eccentricity of the ellipse is