The ellipse can be defined as a conic section with eccentricity lesser than unity. How can you derive the equation of the ellipse using this definition? I can't find proof of the formula using this definition alone.

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    $\begingroup$ With the help of Dandelin Spheres, the section-of-a-cone definition easily gives rise to the sum-of-distances-from-two-points-is-a-constant definition. $\endgroup$ – Blue Dec 24 '15 at 19:30

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