The semi-minor axis,

*b*, is half of the shortest diameter of an ellipse. Together with the semi-major axis,*a*, 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)*: