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 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

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.

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

A square is inscribed inside the ellipse x^2/a^2+y^2/b^2=1 , the length of the side of the square is

The eccentric angles of the vertices of a triangle inscribed in the ellipse x^2/a^2 + y^2/b^2 =1 are alpha, beta, gamma , then for the area of this triangle to be greatest, the angle subtended by the two consecutive vertices of the triangle at the centre of the ellipse in degree measure is...

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 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.

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

PA and PB are tangents drawn from a point P to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 . The area of the triangle formed by the chord of contact AB and axes of co-ordinates is constant. Then locus of P is: