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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).
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. The semi-minor axis b is related to the semi-major axis a through the eccentricity e and the semi-latus rectum, as follows:
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 ...
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.
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]
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. [6]
The universal parabolic constant is the red length divided by the green length. The universal parabolic constant is a mathematical constant. It is defined as the ratio, for any parabola, of the arc length of the parabolic segment formed by the latus rectum to the focal parameter. The focal parameter is twice the focal length. The ratio is ...
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 ...