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:

b^{2} = a^{2}(1-e^{2})

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

or in polar coordinates *(r,θ)*:

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