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) .

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

The eccentricity of the ellipse 5x^(2)+9y^(2)=1 is 2/3 b.3/4 c.4/5 d.1/2

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 1-(1)/(sqrt(2)) (b) 2sqrt(2)-2sqrt(2)-1( d) none of these

The minimum area of triangle formed by tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and the coordinateaxes is