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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:
An ellipse is defined by two axes: the major axis (the longest diameter) of length and the minor axis (the shortest diameter) of length , where the quantities and are the lengths of the semi-major and semi-minor axes respectively.
The length of the chord through one focus, perpendicular to the major axis, ... the x-axis as major axis, and the major/minor semi axis ,. Construction of a directrix ...
The line segments from the origin to these points are called the principal semi-axes of the ellipsoid, because a, b, c are half the length of the principal axes. They correspond to the semi-major axis and semi-minor axis of an ellipse.
For any ellipse, let a be the length of its semi-major axis and b be the length of its semi-minor axis. In the coordinate system with origin at the ellipse's center and x-axis aligned with the major axis, points on the ellipse satisfy the equation + =,
The semi-major axis of the ellipse, a, becomes the equatorial radius of the ellipsoid: the semi-minor axis of the ellipse, b, becomes the distance from the centre to either pole. These two lengths completely specify the shape of the ellipsoid.
The semi-major axis length (a) can be calculated as: ... A radial trajectory can be a double line segment, which is a degenerate ellipse with semi-minor axis = 0 and ...
Also shown are: semi-major axis a, semi-minor axis b and semi-latus rectum p; center of ellipse and its two foci marked by large dots. For θ = 0°, r = r min and for θ = 180°, r = r max. Mathematically, an ellipse can be represented by the formula: = + ,