Tangent Conics

Algebra Level 5

A parabola $$y=x^2$$ is drawn. An ellipse is drawn with one focus at the focus of the parabola and another focus on the line $$y=2014$$. Given that the ellipse is tangent to the parabola at coordinate $$(a,a^2)$$, then find the maximum possible integer value of $$a$$.

Details and Assumptions

• The diagram above is not the correct solution (I just have trouble graphing tilted ellipses to my liking).
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