Focal Parameter

The distance p (sometimes also denoted k) from the focus to the conic section directrix of a conic section. The following table gives the focal parameter for the different types of conics, where a is the semimajor axis, c is the distances from the origin to the focus, and e is the eccentricity.

conic e p

ellipse 0<e<1 (b^2)/(sqrt(a^2-b^2))=(a^2-c^2)/c=(a(1-e^2))/e

parabola e=1 2a

hyperbola e>1 (b^2)/(sqrt(a^2+b^2))=(c^2-a^2)/c=(a(e^2-1))/e

See also

Conic Section, Conic Section Directrix, Eccentricity, Focus, Semilatus Rectum, Universal Parabolic Constant

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Weisstein, Eric W. "Focal Parameter." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FocalParameter.html

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