Question
If the area of the auxiliary circle of the ellipse $ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $ (where $ a > b $) is twice the area of the ellipse, then the eccentricity of the ellipse is ___
If the area of the auxiliary circle of the ellipse $ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $ (where $ a > b $) is twice the area of the ellipse, then the eccentricity of the ellipse is ___