# Quiz 9: Parametric Equations and Polar Coordinates

Mathematics

Q 1Q 1

Write a polar equation in r and of an ellipse with the focus at the origin, with the eccentricity and directrix .
A)
B)
C)
D)
E)

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A

Q 2Q 2

Write a polar equation of the conic that has a focus at the origin, eccentricity , and directrix . Identify the conic.
A) , ellipse
B) , hyperbola
C) , hyperbola
D) , ellipse

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B

Q 3Q 3

Write a polar equation in r and of an ellipse with the focus at the origin, with the eccentricity and vertex at .
A)
B)
C)
D)
E)

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C

Q 4Q 4

Write a polar equation in r and of a hyperbola with the focus at the origin, with the eccentricity and directrix .
A)
B)
C)
D)
E)

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Free

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Q 6Q 6

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.
A) km
B) km
C) km
D) km
E) km

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Multiple Choice

Q 7Q 7

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.
A) AU
B) AU
C) AU
D) AU
E) AU

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Multiple Choice

Q 8Q 8

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.

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Essay

Q 9Q 9

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.

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Essay

Q 10Q 10

The graph of the following curve is given. Find the area that it encloses.
A)A =
B)
C)
D)
E)

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Q 12Q 12

Find the area of the region that lies inside the first curve and outside the second curve.
A)
B)
C)
D)
E)

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Q 17Q 17

Find the polar equation for the curve represented by the given Cartesian equation.
A)
B)
C)
D)
E)

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Q 18Q 18

Find a polar equation for the curve represented by the given Cartesian equation.
A)
B)
C)
D)
E)

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Q 23Q 23

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.

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Q 24Q 24

Set up, but do not evaluate, an integral that represents the length of the parametric curve.

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Q 25Q 25

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.

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