eccentricity
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Eccentricity is a number that describes the shape of a conic section (a curve created by slicing a cone), indicating how much the curve deviates from being a perfect circle. It matters because this single value tells you what type of conic section you're dealing with—whether it's a circle, ellipse, parabola, or hyperbola—and how "stretched" or "open" the shape is.
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A family of conic sections of varying eccentricity share a focus point F and directrix line L, including an ellipse (red, e = 1/2), a parabola (green, e = 1), and a hyperbola (blue, e = 2). The conic of eccentricity 0 in this figure is an infinitesimal circle centered at the focus, and the conic of eccentricity ∞ is an infinitesimally separated pair of lines. A circle of finite radius has an infinitely distant directrix, while a pair of lines of finite separation have an infinitely distant focus.
In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape. One can think of the eccentricity as a measure of how much a conic section deviates from being circular. In particular: