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  2. Ellipse - Wikipedia

    en.wikipedia.org/wiki/Ellipse

    An ellipse (red) obtained as the intersection of a cone with an inclined plane. Ellipse: notations Ellipses: examples with increasing eccentricity. In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.

  3. Focus (geometry) - Wikipedia

    en.wikipedia.org/wiki/Focus_(geometry)

    An ellipse can be defined as the locus of points for which the sum of the distances to two given foci is constant. A circle is the special case of an ellipse in which the two foci coincide with each other. Thus, a circle can be more simply defined as the locus of points each of which is a fixed distance from a single given focus.

  4. Ellipsoid - Wikipedia

    en.wikipedia.org/wiki/Ellipsoid

    The lower part of the diagram shows that F 1 and F 2 are the foci of the ellipse in the xy-plane, too. Hence, it is confocal to the given ellipse and the length of the string is l = 2r x + (a − c). Solving for r x yields r x = ⁠ 1 / 2 ⁠ (l − a + c); furthermore r 2 y = r 2 x − c 2.

  5. Eccentricity (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Eccentricity_(mathematics)

    A family of conic sections of varying eccentricity share a focus point and directrix line, including an ellipse (red, e = 1/2), a parabola (green, e = 1), and a hyperbola (blue, e = 2). The conic of eccentricity 0 in this figure is an infinitesimal circle centered at the focus, and the conic of eccentricity ∞ is an infinitesimally separated ...

  6. Elliptic coordinate system - Wikipedia

    en.wikipedia.org/wiki/Elliptic_coordinate_system

    In geometry, the elliptic coordinate system is a two-dimensional orthogonal coordinate system in which the coordinate lines are confocal ellipses and hyperbolae. The two foci F 1 {\displaystyle F_{1}} and F 2 {\displaystyle F_{2}} are generally taken to be fixed at − a {\displaystyle -a} and + a {\displaystyle +a} , respectively, on the x ...

  7. Generalized conic - Wikipedia

    en.wikipedia.org/wiki/Generalized_conic

    The starting point for this approach is to look upon an ellipse as a curve satisfying the 'two-focus property': an ellipse is a curve that is the locus of points the sum of whose distances from two given points is constant. The two points are the foci of the ellipse. The curve obtained by replacing the set of two fixed points by an arbitrary ...

  8. Semi-major and semi-minor axes - Wikipedia

    en.wikipedia.org/wiki/Semi-major_and_semi-minor_axes

    The semi-minor axis of an ellipse runs from the center of the ellipse (a point halfway between and on the line running between the foci) to the edge of the ellipse. The semi-minor axis is half of the minor axis. The minor axis is the longest line segment perpendicular to the major axis that connects two points on the ellipse's edge.

  9. Focal conics - Wikipedia

    en.wikipedia.org/wiki/Focal_conics

    A,C: vertices of the ellipse and foci of the hyperbola E,F: foci of the ellipse and vertices of the hyperbola Focal conics: two parabolas A: vertex of the red parabola and focus of the blue parabola F: focus of the red parabola and vertex of the blue parabola. In geometry, focal conics are a pair of curves consisting of [1] [2] either