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Key concepts
Any conic may be determined by a single focus, the corresponding eccentricity, and the directrix. We can also define a conic in terms of a fixed point, the focus
at the pole, and a line, the directrix, which is perpendicular to the polar axis.
A conic is the set of all points
where eccentricity
is a positive real number. Each conic may be written in terms of its polar equation. See
[link] .
The polar equations of conics can be graphed. See
[link] ,
[link] , and
[link] .
Conics can be defined in terms of a focus, a directrix, and eccentricity. See
[link] and
[link] .
We can use the identities
and
to convert the equation for a conic from polar to rectangular form. See
[link] .
Section exercises
Verbal
Explain how eccentricity determines which conic section is given.
If eccentricity is less than 1, it is an ellipse. If eccentricity is equal to 1, it is a parabola. If eccentricity is greater than 1, it is a hyperbola.
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Ahmad
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