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Eccentricity

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Algebra and Trigonometry

Definition

Eccentricity measures the deviation of a conic section from being circular. It is a non-negative real number that uniquely defines the shape of the conic.

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5 Must Know Facts For Your Next Test

  1. For a circle, the eccentricity is 0, indicating no deviation from circularity.
  2. An ellipse has an eccentricity between 0 and 1, exclusive.
  3. A parabola has an eccentricity exactly equal to 1.
  4. A hyperbola has an eccentricity greater than 1.
  5. The formula for eccentricity $e$ in polar coordinates is given by $e = \frac{c}{a}$ where $c$ is the distance from the center to a focus and $a$ is the semi-major axis.

Review Questions

  • What is the eccentricity of a circle?
  • How does the value of eccentricity determine whether a conic section is an ellipse or a hyperbola?
  • Write the formula for calculating eccentricity in polar coordinates.
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