Find the area of the greatest rectangle ...

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

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Find the area of the equilateral triangle that can be inscribed in the circle : x^2 + y^2- 4x + 6y -3=0 .

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 smaller region bounded by the ellipse x^2/a^2 + y^2/b^2 = 1 and the straight line x/a + y/b = 1 (using integration)

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.

Area of ellipse x^2/a^2 + y^2/b^2 = 1, a > b is :

Find the locus of the vertices of equilateral triangle circumscribing the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 .

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