The ratio of the area of triangle inscribed in ellipse `x^2/a^2+y^2/b^2=1` to that of triangle formed by the corresponding points on the auxiliary circle is 0.5. Then, find the eccentricity of the ellipse. (A) `1/2` (B) `sqrt3/2` (C) `1/sqrt2` (D) `1/sqrt3`

The ratio of any triangle PQR inscribed in an ellipse x^2/a^2+y^2/b^2=1 and that of triangle formed by the corresponding points on the auxilliary circle is b/a .

Show that the area of triangle inscribed in an ellipse bears a constant ratio to the area of thetriangle formed by joining points on the auxiliary circle corresponding to the vertices of the firsttriangle.

There are exactly two points on the ellipse x^2/a^2+y^2/b^2=1 ,whose distance from its centre is same and equal to sqrt((a^2+2b^2)/2) . The eccentricity of the ellipse is: (A) 1/2 (B) 1/sqrt2 (C) sqrt2/3 (D) sqrt3/2

Pa n dQ are the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and B is an end of the minor axis. If P B Q is an equilateral triangle, then the eccentricity of the ellipse is 1/(sqrt(2)) (b) 1/3 (d) 1/2 (d) (sqrt(3))/2

Pa n dQ are the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and B is an end of the minor axis. If P B Q is an equilateral triangle, then the eccentricity of the ellipse is 1/(sqrt(2)) (b) 1/3 (d) 1/2 (d) (sqrt(3))/2

A parabola is drawn with focus at one of the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 . If the latus rectum of the ellipse and that of the parabola are same, then the eccentricity of the ellipse is (a) 1-1/(sqrt(2)) (b) 2sqrt(2)-2 (c) sqrt(2)-1 (d) none of these

The eccentric angles of the vertices A, B, C of a triangle inscribed in the ellipse x^2/4^2 + y^2/1^2 = 1 are alpha, beta, gamma . Let P, Q, R be the points on the auxiliary circle corresponding to points A, B, C respectively of the ellipse. (ar(DeltaPQR))/(ar(DeltaABC))= (A) 2 (B) 4 (C) 9 (D) 26

The eccentricity of the ellipse 25x^2+16 y^2=400 is a. 3//5 b. 1//3 c. 2//5 d. 1//5

There are exactly two points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 whose distances from its center are the same and are equal to (sqrt(a^2+2b^2))/2dot Then the eccentricity of the ellipse is 1/2 (b) 1/(sqrt(2)) (c) 1/3 (d) 1/(3sqrt(2))

The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is such that it has the least area but contains the circle (x-1)^(2)+y^(2)=1 The eccentricity of the ellipse is