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In geometry, a multifocal ellipse (also known as n-ellipse, k-ellipse, polyellipse, egglipse, generalized ellipse, and (in German) Tschirnhaus'sche Eikurve) is a generalization of an ellipse with multiple foci.

More concretely, and given n points in a plane (foci), an n-ellipse is the locus of all points of the plane whose sum of distances to the n foci is a constant. The set of points of an n-ellipse is defined as:

\left\{(x, y) \in R^2: \sum_{i=1}^n \sqrt{(x-u_i)^2 + (y-v_i)^2} = d\right\}

The 1-ellipse corresponds to the circle. The 2-ellipse corresponds to the classic ellipse. Both are algebraic curves of degree 2.


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