Eccentricity of an ellipse

An ellipse which is not a circle has eccentricity \(0 < e < 1\). (A circle has eccentricity \(0\).) The ellipse with equation \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\] where \(a > b\), has eccentricity \(e\) given by \[b^2 = a^2(1 - e^2).\]