$$ \text { The area of the region enclosed by the curve }\left\{(x, y): 4 x^2+25 y^2=100\right\} \text { is } $$

The equation of an ellipse, whose focus is $$(1,0)$$, directrix is $$x=4$$ and whose eccentricity is a root of the quadratic equation $$2 x^2-3 x+1=0$$, is

If the length of the major axis of an ellipse is 3 times the length of the minor axis, then its eccentricity is

If the area of the auxillary circle of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1(a > b)$$ is twice the area of the ellipse, then the eccentricity of the ellipse is