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)*: