Major / minor axis of an ellipse - Math Open Reference

The major and minor axes of an ellipse are diameters (lines through the center) of the ellipse. The major axis is the longest diameter and the minor 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 is the perpendicular bisector of the other. That is, each axis cuts the other into two equal parts, and each axis crosses the other at right angles.

The focus points always lie on the major (longest) axis, spaced equally each side of the center. See Foci (focus points) of an ellipse

Calculating the axis lengths

Recall that an ellipse is defined by the position of the two focus points (foci) and the sum of the distances from them to any point on the ellipse. (See Ellipse definition and properties). Referring to the figure on the right, if you were drawing an ellipse using the string and pin method, the string length would be a+b, and the distance between the pins would be f.

The length of the minor axis is given by the formula:

where
f is the distance between foci
a,b are the distances from each focus to any point on the ellipse

The length of the major axis is given by the formula:

where
a,b are the distances from each focus to any point on the ellipse

Other ellipse topics