If ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` is rotated `90^(@)` about origin,the equation of ellipse after rotation is

The area of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is

If a^(2) + b^(2) = 25 and a focus of the ellipse (x^(2))/(a^(2) + 3) + (y^(2))/(b^(2) + 3) = 1 is (sqrt(7) ,0) , then equation of this ellipse is

Find the area of the region bounded by the latus recta of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and the targets to the ellipse drawn at their ends

If the focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1, is normal at (a cos theta,b sin theta) then eccentricity of the ellipse is

If the area of the auxiliary circle of the ellipse (x ^(2))/(a ^(2)) + (y ^(2))/(b ^(2)) =1 (a gt b) is twice the area of the ellipse, then the eccentricity of the ellipse is

Prove that the area bounded by the circle x^(2)+y^(2)=a^(2) and the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is equal to the area of another ellipse having semi-axis a-b and b,a>b

The value of a for the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1,(a>b), if the extremities of the latus rectum of the ellipse having positive ordinates lie on the parabola x^(2)=2(y-2) is

if the line x- 2y = 12 is tangent to the ellipse (x^(2))/(b^(2))+(y^(2))/(b^(2))=1 at the point (3,(-9)/(2)) then the length of the latusrectum of the ellipse is

Chords of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 are drawn through the positive end of the minor axis. Then prove that their midpoints lie on the ellipse.