N-ellipse

In geometry, the n"-ellipse is a generalization of the ellipse allowing more than two foci. "n"-ellipses go by numerous other names, including multifocal ellipse, polyellipse, egglipse, k"-ellipse, and Tschirnhaus'sche Eikurve (after Ehrenfried Walther von Tschirnhaus). They were first investigated by James Clerk Maxwell in 1846.
Given "n" points ("u""i", "v""i") (called foci) in a plane, an "n"-ellipse is the locus of all points of the plane whose sum of distances to the "n" foci is a constant "d". In formulas, this is the set
The 1-ellipse is the circle. The 2-ellipse is the classic ellipse. Both are algebraic curves of degree 2.
For any number "n" of foci, the "n"-ellipse is a closed, convex curve. The curve is smooth unless it goes through a focus. 
The "n"-ellipse is in general a subset of the points satisfying a particular algebraic equation. If "n" is odd, the algebraic degree of the curve is formula_2, while if "n" is even the degree is formula_3.
"n"-ellipses are special cases of spectrahedra.