Let x^(2)=4ky,k gt 0 be a parabola with ...

Let `x^(2)=4ky,k gt 0` be a parabola with vertex A. Let BC be its latus rectum. An ellipse with center on BC touches the parabola at A, and cuts BC at point D and E such that BD=DE=EC (B,D,E,C in that order). The eccentricity of the ellipse is

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