KVPY SX SB Exam 2018 Question Paper

Let ${\mathit{x}}^2=4\mathit{k}\mathit{y},\mathit{k}>0$, 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 points D and E such that BD = DE = EC (B, D, E, C in that order).
The eccentricity of the ellipse is