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sec10_6

# sec10_6 - ± e sin θ 1 Section 10.6 Conic Sections in...

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10.6 Conic Sections in Polar Coordinates 1. Polar Coordinates Theorem 1.1 (p.662) . Let F be a fxed point, called the focus , and let ± be a fxed line, called the directrix , in a plane. Let e be a positive number, called the eccentricity . The set oF all points P in the plane such that d ( P,F ) d ( P,± ) = e is a conic section . The conic section is (1) an ellipse iF e< 1 (2) a parabola iF e =1 (3) a hyperbola iF e> 1 Theorem 1.2. A polar equation oF the Form below represents a conic section with eccentricity e . The conic section is an ellipse iF e< 1 , a parabola iF e =1 , and a hyperbola iF e> 1 ; r = ed 1 ± e cos θ , or r = ed 1

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Unformatted text preview: ± e sin θ . 1 Section 10.6 Conic Sections in Polar Coordinates 2 2. Examples Example 2.1. (problem 2) Write the polar equation of the parabola with the focus at the origin and directrix x = 4 . Example 2.2. (problem 4) Write the polar equation of the hyperbola with the focus at the origin, eccentricity 2 and directrix y =-2 . Example 2.3. (problem 10) (a) Find the eccentricity, (b) identify the conic, (c) give an equation of the directrix, and (d) sketch the conic. r = 12 3-10 cos θ Example 2.4....
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sec10_6 - ± e sin θ 1 Section 10.6 Conic Sections in...

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