A circle concentric with the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` and passes through the foci `F_1a n dF_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 `P F_1F_2` is 26, then find the valueof `4a^2-4b^2dot`

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 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

The line 2x+y=3 intersects the ellipse 4x^(2)+y^(2)=5 at two points. The point of intersection of the tangents to the ellipse at these point is

Let P be a variable on the ellipse (x^(2))/(25)+ (y^(2))/(16) =1 with foci at F_(1) and F_(2)

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

Number of points on the ellipse x^2/a^2+y^2/b^2=1 at which the normal to the ellipse passes through at least one of the foci of the ellipse is

" Eccentricity of ellipse " (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 " such that the line joining the foci subtends a right angle only at two points on ellipse is "

Let P be a variable point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with foci F_1" and "F_2 . If A is the area of the trianglePF_1F_2 , then the maximum value of A is

P is a variable point on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=2backslash(a>b) whose foci are F_(1) and F_(2.) The maximum area (in unit' ) of the Delta PFF' is

Find the equation of the tangents at the ends of the latus rectum of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and also show that they pass through the points of intersection of the major axis and directrices.