Semimajor / Semiminor axis of an ellipse
From Latin: semi "half"
Semimajor axis: The longest radius of an ellipse.
Semiminor axis: The shortest radius of an ellipse.
Try this Drag any orange dot. The ellipse changes shape as you change the length of the major or minor axis.
The semimajor and semiminor axes of an ellipse are radii of the ellipse (lines from the center to the ellipse).
The semimajor axis is the longest radius and the semiminor axis the shortest. If they are equal in length then the ellipse is a circle. Drag any
orange dot in the figure above until this is the case.
Each axis always meets the other at the center at right angles.
The focus points always lie on the major (longest) axis, spaced equally each side of the center. So one will always lie on the semimajor axis.
See Foci (focus points) of an ellipse. In the figure above, reshape the ellipse and note the behavior of the two black focus points.
Calculating the axis lengths
The semimajor and semiminor axes are half the length of the major and minor axis.
To calculate their lengths, use one of the formulae at Major / Minor Axis of an ellipse and divide by two.
Definition note
Some find the names 'semimajor / semiminor axis' cumbersome and confusing.
Typically, an axis passes all the way through an object and is an axis of symmetry.
In the semi case that is not so.
Also, they are usually used as a length (see Area of an ellipse) rather than a line segment.
For these reasons, some prefer to call them the major radius and minor radius of the ellipse.
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