If the area of the auxillary circle of the ellipse x² a² + y² b² =1(a>b) is twice the area of the ellipse, then the eccentricity of the ellipse is

Step-by-step solution

Given, ellipse is x² a² + y² b² =1 , whose area is 2 a b . The auxillary circle of the ellipse is x²+y²=a² whose area is a² . Given that, a²=2 a b a=2 b Now, eccentricity of ellipse aligned &= 1- b² a² &= 1- b² 4 b² &= 4-1 4 = 3 2 aligned