Which of the following is defined as the first eccentricity of an ellipse?

• A. First eccentricity
• B. Second eccentricity
• C. Angular eccentricity
• D. Flattening

Answer: (A)

The main idea here is the first eccentricity, a number that tells how stretched an ellipse is. If you have an ellipse with semi-major axis a, semi-minor axis b, and c as the distance from the center to a focus, the first eccentricity is the ratio e = c/a. Since c^2 = a^2 − b^2, you can also write e = sqrt(1 − (b^2)/(a^2)). This value always lies between 0 and 1: e = 0 only for a circle (a = b), and e gets closer to 1 as the ellipse becomes more elongated.

The term you might hear as the “second eccentricity” is a different quantity, defined as e' = c/b, which is not the same as the first eccentricity. There are other related parameters as well, like angular eccentricity and flattening f = (a − b)/a, which are tied to the geometry in other ways but do not define the first eccentricity.