Semi-major Axis

An ellipse with semi-major axis, a.

The semi-major axis, a, is half of the longest diameter of an ellipse. Together with the semi-minor axis , b, and eccentricity, e, it forms a set of related values that completely describe the shape of an ellipse:

b2 = a2(1-e2)

In cartesian coordinates (x,y), an ellipse is the solution of:

$ \left(\frac xa\right)^2 + \left(\frac yb\right)^2 = 1 $

or in polar coordinates (r,θ):

$ r = \frac{a(1-e^2)}{1+e\cos\theta} $

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