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)*:

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