Exam 9: Extension E: Vectors and the Geometry of Space

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Consider the polar equation Consider the polar equation   (a)Find the eccentricity and an equation of the directrix of the conic. (b)Identify the conic. (c)Sketch the curve. (a)Find the eccentricity and an equation of the directrix of the conic. (b)Identify the conic. (c)Sketch the curve.

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(a)eccentricity: 2,directrix: (a)eccentricity: 2,directrix:      (b)hyperbola (c)  (a)eccentricity: 2,directrix:      (b)hyperbola (c)
(b)hyperbola
(c) (a)eccentricity: 2,directrix:      (b)hyperbola (c)

Consider the polar equation Consider the polar equation    (a)Find the eccentricity and an equation of the directrix of the conic. (b)Identify the conic. (c)Sketch the curve. (a)Find the eccentricity and an equation of the directrix of the conic. (b)Identify the conic. (c)Sketch the curve.

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(a)eccentricity: (a)eccentricity:   ,directrix:      (b)parabola (c)  ,directrix: (a)eccentricity:   ,directrix:      (b)parabola (c)  (a)eccentricity:   ,directrix:      (b)parabola (c)
(b)parabola
(c) (a)eccentricity:   ,directrix:      (b)parabola (c)

Write a polar equation of the conic that has a focus at the origin,eccentricity Write a polar equation of the conic that has a focus at the origin,eccentricity   ,and directrix   Identify the conic. ,and directrix Write a polar equation of the conic that has a focus at the origin,eccentricity   ,and directrix   Identify the conic. Identify the conic.

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B

Find the eccentricity of the conic. Find the eccentricity of the conic.

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The orbit of Hale-Bopp comet,discovered in 1995,is an ellipse with eccentricity The orbit of Hale-Bopp comet,discovered in 1995,is an ellipse with eccentricity   and one focus at the Sun.The length of its major axis is   AU.[An astronomical unit (AU)is the mean distance between Earth and the Sun,about 93 million miles.] Find the maximum distance from the comet to the Sun.(The perihelion distance from a planet to the Sun is   and the aphelion distance is   )Find the answer in AU and round to the nearest hundredth. and one focus at the Sun.The length of its major axis is The orbit of Hale-Bopp comet,discovered in 1995,is an ellipse with eccentricity   and one focus at the Sun.The length of its major axis is   AU.[An astronomical unit (AU)is the mean distance between Earth and the Sun,about 93 million miles.] Find the maximum distance from the comet to the Sun.(The perihelion distance from a planet to the Sun is   and the aphelion distance is   )Find the answer in AU and round to the nearest hundredth. AU.[An astronomical unit (AU)is the mean distance between Earth and the Sun,about 93 million miles.] Find the maximum distance from the comet to the Sun.(The perihelion distance from a planet to the Sun is The orbit of Hale-Bopp comet,discovered in 1995,is an ellipse with eccentricity   and one focus at the Sun.The length of its major axis is   AU.[An astronomical unit (AU)is the mean distance between Earth and the Sun,about 93 million miles.] Find the maximum distance from the comet to the Sun.(The perihelion distance from a planet to the Sun is   and the aphelion distance is   )Find the answer in AU and round to the nearest hundredth. and the aphelion distance is The orbit of Hale-Bopp comet,discovered in 1995,is an ellipse with eccentricity   and one focus at the Sun.The length of its major axis is   AU.[An astronomical unit (AU)is the mean distance between Earth and the Sun,about 93 million miles.] Find the maximum distance from the comet to the Sun.(The perihelion distance from a planet to the Sun is   and the aphelion distance is   )Find the answer in AU and round to the nearest hundredth. )Find the answer in AU and round to the nearest hundredth.

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The planet Mercury travels in an elliptical orbit with eccentricity The planet Mercury travels in an elliptical orbit with eccentricity   Its minimum distance from the Sun is   km.If the perihelion distance from a planet to the Sun is   and the aphelion distance is   ,find the maximum distance (in km)from Mercury to the Sun. Its minimum distance from the Sun is The planet Mercury travels in an elliptical orbit with eccentricity   Its minimum distance from the Sun is   km.If the perihelion distance from a planet to the Sun is   and the aphelion distance is   ,find the maximum distance (in km)from Mercury to the Sun. km.If the perihelion distance from a planet to the Sun is The planet Mercury travels in an elliptical orbit with eccentricity   Its minimum distance from the Sun is   km.If the perihelion distance from a planet to the Sun is   and the aphelion distance is   ,find the maximum distance (in km)from Mercury to the Sun. and the aphelion distance is The planet Mercury travels in an elliptical orbit with eccentricity   Its minimum distance from the Sun is   km.If the perihelion distance from a planet to the Sun is   and the aphelion distance is   ,find the maximum distance (in km)from Mercury to the Sun. ,find the maximum distance (in km)from Mercury to the Sun.

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Write a polar equation in r and Write a polar equation in r and   of an ellipse with the focus at the origin,with the eccentricity   and vertex at  of an ellipse with the focus at the origin,with the eccentricity Write a polar equation in r and   of an ellipse with the focus at the origin,with the eccentricity   and vertex at  and vertex at Write a polar equation in r and   of an ellipse with the focus at the origin,with the eccentricity   and vertex at

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Write a polar equation in r and Write a polar equation in r and   of a hyperbola with the focus at the origin,with the eccentricity   and directrix  of a hyperbola with the focus at the origin,with the eccentricity Write a polar equation in r and   of a hyperbola with the focus at the origin,with the eccentricity   and directrix  and directrix Write a polar equation in r and   of a hyperbola with the focus at the origin,with the eccentricity   and directrix

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Write a polar equation in r and θ\theta of an ellipse with the focus at the origin,with the eccentricity  Write a polar equation in r and  \theta  of an ellipse with the focus at the origin,with the eccentricity   and directrix   and directrix  Write a polar equation in r and  \theta  of an ellipse with the focus at the origin,with the eccentricity   and directrix

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