# Do you like ellipse?

Geometry Level 4

Let $$k$$ be the ratio of the area of an ellipse $$A_e$$ to the area of the triangle $$A_t$$ the ellipse is inscribed in; that is: $k=\dfrac {A_e} {A_t} .$

Given that the maximum value of $$k$$ has a closed form, find this closed form.