10.6_bzat4e

# 10.6_bzat4e - θ-r 2 4 6 8 10 12 x y Problem continued from...

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Section 10.6 Conic Sections in Polar Coordinates

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The Focus-Directrix Definitions of the Conic Sections

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Polar Equations of Conics

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Example 2 Graph the polar equation r= Where is the vertex? 1 sin θ + -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 x y Problem continued on the next slide.

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Example 2 Graph the polar equation r= 1 sin θ + 1 2 3 4 5 x y r θ Problem continued from the previous slide.
Example 4 Graph the polar equation r= Where are the vertices? 2 cos θ - -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 x y Problem continued on the next slide.

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Example 4 Graph the polar equation r= 2 cos θ - 1 2 3 4 5 x y r θ Problem continued from the previous slide.
Example 12 Graph the polar equation r= Where are the vertices? 2 3sin θ - -12 -8 -4 4 8 12 -8 -4 4 8 x y Problem continued on the next slide.

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Example 12 Graph the polar equation r= 2 3sin θ - r θ 2 4 6 8 10 12 x y Problem continued from the previous slide.
Example 12 Graph the polar equation r= Where are the vertices? 2 3sin θ - -12 -8 -4 4 8 12 -8 -4 4 8 x y Problem continued on the next slide.

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Example 12 Graph the polar equation r=

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Unformatted text preview: θ-r 2 4 6 8 10 12 x y Problem continued from the previous slide. Example 6 Graph the polar equation r= Where are the vertices? 3 2cos θ--6-5-4-3-2-1 1 2 3 4 5 6-6-5-4-3-2-1 1 2 3 4 5 x y Problem continued on the next slide. Example 6 Graph the polar equation r= 3 2cos θ-r 2 4 6 8 10 12 x y Problem continued from the previous slide. (a) (b) (c) (d) 6 Identify the conic, find e and p. r= 3 1 cos 2 θ + 3 , 6 2 3 e= - , p=4 2 3 , , p=4 2 3 , p=6 2 hyperbola e p ellipse hyperbola e ellipse e = = = = (a) (b) (c) (d) 6 Find the vertices of the following conic r= 3 1 cos 2 θ + ( 29 ( 29 ( 29 ( 29 12,0 6, 12 ,0 12, 5 6,0 12, 2 12 3 , 12, 5 2 2 π- - ÷ - ÷ - ÷ ÷ Continuation of the previous problem....
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