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Ellipse

Ellipse

Geometric figure in which the sum of the distances of each point P from two fixed points F1 and F2, called the foci, is constant.

  • Consider an ellipse with foci F1 and F2 and points P1 and P2 :
    d(P1, F1) + d(P1, F2) = d(P2, F1) + d(P2, F2)

ellipse

  • Segments a and b in the illustration are the semi-minor axis (conjugate axis) and the semi-major axis (transverse axis) of the ellipse. The major axis (transverse axis) is the diameter of the ellipse.
  • An ellipse can also be formed by the intersection of a cone of revolution with a plane that meets all the generating lines and that does not pass through the apex.

Formula

The area A of an ellipse of semi-axes a and b is : A = πab.

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