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

Equation of ellipse is x² a² + y² b² =1 Then, equation of auxillary circle will be x²+y²=a² (a>b) Now, it is given that Area of auxillary circle =2 Area of ellipse array ll & a²=2 a b & a=2 b array Now, cocentricity of the ellipse, aligned e &= 1- b² a² = 1- b² (2 b)² &= 1- b² 4 b² = 1- 1 4 = 3 2 aligned