Majoraxis

Major axis, sometimes written as majoraxis, is a term in geometry referring to the longest diameter of an ellipse. It passes through the center of the ellipse and through its two foci. The endpoints of the major axis are the ellipse’s vertices. For an ellipse with semi-major axis a and semi-minor axis b, where a ≥ b, the length of the major axis is 2a, and the distance from the center to either focus is c = sqrt(a^2 − b^2). The eccentricity is e = c/a = sqrt(1 − (b^2/a^2)). The minor axis, perpendicular to the major axis, has length 2b.

In standard position, with the major axis aligned with the x-axis, the ellipse is x^2/a^2 + y^2/b^2 = 1. If the ellipse is rotated by an angle θ, the equation in Cartesian coordinates becomes a rotated quadratic form; the major axis remains the line through the center along which curvature is maximum and along which the foci lie. The major and minor axes are the eigenvectors of the ellipse’s quadratic form and are symmetry axes of the figure.

Applications: In geometry and physics, the semi-major axis a is a key parameter; for orbital mechanics, the semi-major axis describes the size of an elliptic orbit. In astronomy and image analysis, the term major axis appears in describing the apparent orientation and extent of elongated objects such as galaxies or fitted ellipses to blobs, with the axial ratio b/a used as a measure of elongation.

Notes: The term is most commonly used for ellipses; for other conic sections, related terms like transverse axis may be used, but “major axis” is standard for ellipses. Some software or literature may spell it as majoraxis.