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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For a circle, the eccentricity is 0, indicating no deviation from circularity.
An ellipse has an eccentricity between 0 and 1, exclusive.
A parabola has an eccentricity exactly equal to 1.
A hyperbola has an eccentricity greater than 1.
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.
Related terms
Conic Sections: Shapes created by intersecting a plane with a double-napped cone; includes circles, ellipses, parabolas, and hyperbolas.
Focus: A point used to define and construct conic sections; each type of conic has one or two foci.
Directrix: $\text{For conics in polar coordinates, it’s } y = k \text{ or } x = h \text{ line used along with focus to define conics.}$