astronomy questions

Question

if an ellipse has an eccentricity of 0, then what must be true of its component numbers, and what is the shape of this ellipse ?

Answer 1

The eccentricity of an ellipse is defined as ε = c/a, with c the linear eccentricity (the distance between the center of the ellips and a focal point) and a the semi-major axis (half the length of the major axis).

c² = a² - b², with b the semi-minor axis.

If the eccentricity is 0, this means that c = 0 (and a = b), thus the focal points are the center of the ellipse, making it a circle.