The major and minor axes of an ellipse are perpendicular to each other and to the tangent lines to the ellipse at the points where the axes intersect the ellipse.

In the mathematical fields of geometry and linear algebra, a principal axis is a certain line in a Euclidean space associated to an ellipsoid or hyperboloid, generalizing the major and minor axes of an ellipse.

Another method is using Rytz's construction, which takes advantage of the Thales' theorem for finding the directions and lengths of the major and minor axes of an ellipse regardless of its rotation or shearing.

A conjugate axis of length 2b, corresponding to the minor axis of an ellipse, is sometimes drawn on the non-transverse principal axis; its endpoints b lie on the minor axis at the height of the asymptotes over/under the hyperbola's vertices.