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.

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 .

Find the area of the greatest rectangle that can be inscribed in an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 .

Find the area of the greatest rectangle that can be inscribed in an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1

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.

Find the maximum area of an isosceles triangle inscribed in the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with its vertex at one end of the major axis.

The point of intersection of the tangents at the point P on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and its corresponding point Q on the auxiliary circle meet on the line (a) x=a/e (b) x=0 (c) y=0 (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 area of the parallelogram inscribed in the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 , whose diaonals are the conjugate diameters of the ellipse is given by

Find the area of equilateral triangle inscribed in a circle x^2+y^2+2gx+2fy+c=0

If the area of the ellipse ((x^2)/(a^2))+((y^2)/(b^2))=1 is 4pi , then find the maximum area of rectangle inscribed in the ellipse.