Answer
You should graciously remind them of the definition of eccentricity of an
ellipse. Namely, the eccentricity of an ellipse is given by the distance
between the foci divided by the distance between the vertices. Since
the foci are always inside the ellipse and the vertices are on its outer edge,
you know that the ratio of the two must be less than 1. Hence, your
colleague's eccentricity of 5.673 cannot be correct. As a matter of
fact, any number greater than 1, no matter how close to 1, cannot be the
eccentricity of an ellipse.
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James A. Sellers