Eccentricity

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Conic Sections
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Eccentricity

• Eccentricity of a conic section is a non-negative
  real number that measures its deviation from a
  circle. Hence
• A circle has eccentricity 0,
• An ellipse has eccentricity between 0 and 1,
• A parabola has eccentricity exactly 1,
• A hyperbola has eccentricity bigger than 1.
• A more precise definition comes next.

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Definition of eccentricity Pick any point P on
the curve, the eccentricity of the conic curve is
P
focus
directrix
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e 0.2
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e 0.4
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e 0.6
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e 0.8
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e 1.0
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Polar equation of a conic section
The pole is always chosen at a focus of the
conic, and there are two choices according to
whether you want the directrix to be vertical or
horizontal (1) Vertical directrix
(2) Horizontal directrix
where e is the eccentricity and d is the
perpendicular distance between the pole and the
nearest directrix
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