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  2. Parabola - Wikipedia

    en.wikipedia.org/wiki/Parabola

    The latus rectum is defined similarly for the other two conics – the ellipse and the hyperbola. The latus rectum is the line drawn through a focus of a conic section parallel to the directrix and terminated both ways by the curve. For any case, is the radius of the osculating circle at the vertex. For a parabola, the semi-latus rectum, , is ...

  3. Ellipse - Wikipedia

    en.wikipedia.org/wiki/Ellipse

    The length of the chord through one focus, perpendicular to the major axis, is called the latus rectum. One half of it is the semi-latus rectum. A calculation shows: [4] = = (). The semi-latus rectum is equal to the radius of curvature at the vertices (see section curvature).

  4. Hyperbola - Wikipedia

    en.wikipedia.org/wiki/Hyperbola

    The length of the chord through one of the foci, perpendicular to the major axis of the hyperbola, is called the latus rectum. One half of it is the semi-latus rectum. A calculation shows =. The semi-latus rectum may also be viewed as the radius of curvature at the vertices.

  5. 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.

  6. Method of exhaustion - Wikipedia

    en.wikipedia.org/wiki/Method_of_exhaustion

    The area bounded by the intersection of a line and a parabola is 4/3 that of the triangle having the same base and height (the quadrature of the parabola); The area of an ellipse is proportional to a rectangle having sides equal to its major and minor axes;

  7. Conic section - Wikipedia

    en.wikipedia.org/wiki/Conic_section

    The type of the conic is determined by the type of cone, that is, by the angle formed at the vertex of the cone: If the angle is acute then the conic is an ellipse; if the angle is right then the conic is a parabola; and if the angle is obtuse then the conic is a hyperbola (but only one branch of the curve). [27]

  8. Perimeter of an ellipse - Wikipedia

    en.wikipedia.org/wiki/Perimeter_of_an_ellipse

    In more recent years, computer programs have been used to find and calculate more precise approximations of the perimeter of an ellipse. In an online video about the perimeter of an ellipse, recreational mathematician and YouTuber Matt Parker, using a computer program, calculated numerous approximations for the perimeter of an ellipse. [10]

  9. Kepler orbit - Wikipedia

    en.wikipedia.org/wiki/Kepler_orbit

    The distance to the focal point is a function of the polar angle relative to the horizontal line as given by the equation In celestial mechanics , a Kepler orbit (or Keplerian orbit , named after the German astronomer Johannes Kepler ) is the motion of one body relative to another, as an ellipse , parabola , or hyperbola , which forms a two ...