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

Step-by-step solution

Equation of auxiliary circle of the ellipse, x² a² + y² b² =1 is x²+y²=a² Area of auxiliary circle = a² and area of an ellipse = a b Now, according to the question aligned a²=2( a b) a b &=2 b b= a 2 ...(i) aligned Eccentricity of an ellipse aligned &= a²-b² a² = a²- a² 4 a² [from Eq. (i)] &= 3 a² 4 a² = 3 2 aligned