Calculus Early Transcendentals

Mathematics

Quiz 9 :

Parametric Equations and Polar Coordinates

Quiz 9 :

Parametric Equations and Polar Coordinates

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The graph of the following curve is given. Find the area that it encloses. img img
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D

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Find the area of the region that lies inside the first curve and outside the second curve. img
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E

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Consider the polar equation img .(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: img img (b) hyperbola
(c) img

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Find the area that the curve encloses. img img
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The orbit of Hale-Bopp comet, discovered in 1995, is an ellipse with eccentricity img and one focus at the Sun. The length of its major axis is img 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 img and the aphelion distance is img .) Find the answer in AU and round to the nearest hundredth.
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Write a polar equation of the conic that has a focus at the origin, eccentricity img , and directrix img . Identify the conic.
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The planet Mercury travels in an elliptical orbit with eccentricity img . Its minimum distance from the Sun is img km. If the perihelion distance from a planet to the Sun is img and the aphelion distance is img , find the maximum distance (in km) from Mercury to the Sun.
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Find a polar equation for the curve represented by the given Cartesian equation. img
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Write a polar equation in r and of an ellipse with the focus at the origin, with the eccentricity img and directrix img .
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Consider the polar equation img .(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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Find the area enclosed by the curve img .
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Find the length of the polar curve. img
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Write a polar equation in r and img of a hyperbola with the focus at the origin, with the eccentricity img and directrix img .
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Find the area of the region enclosed by one loop of the curve. img
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Find the Cartesian coordinates of the point img .
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Find the eccentricity of the conic. img
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Write a polar equation in r and img  of an ellipse with the focus at the origin, with the eccentricity img and vertex at img .
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Sketch the polar curve with the given equation. img
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Find the polar equation for the curve represented by the given Cartesian equation. img
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Find a Cartesian equation for the curve described by the given polar equation. img
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