Deck 9: Parametric Equations and Polar Coordinates

Question 1

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

A)A =
B)
C)
D)
E)

Answer 1

Question 2

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

A)
B)
C)
D)
E)

Answer 2

Question 3

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.

Answer 3

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

Question 4

Find the area that the curve encloses.

Question 5

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

Question 6

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

Question 7

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

Question 8

Find a polar equation for the curve represented by the given Cartesian equation.

A)
B)
C)
D)
E)

Question 9

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

A)
B)
C)
D)
E)

Question 10

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.

Question 11

Find the area enclosed by the curve .

Question 12

Find the length of the polar curve.

A)
B)
C)
D)
E)None of these

Question 13

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)

Question 14

Find the area of the region enclosed by one loop of the curve.

A)
B)
C)
D)
E)

Question 15

Find the Cartesian coordinates of the point .

A)
B)
C)
D)
E)

Question 16

Find the eccentricity of the conic.

A)
B)
C)
D)
E)

Question 17

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

A)
B)
C)
D)
E)

Question 18

Sketch the polar curve with the given equation.

A)
B)
C)
D)

Question 19

Find the polar equation for the curve represented by the given Cartesian equation.

A)
B)
C)
D)
E)

Question 20

Find a Cartesian equation for the curve described by the given polar equation.

Question 21

Match the parametric equations with the graphs labeled a-e.

A)
B)
C)
D)
E)

Question 22

Find the length of the curve. , ,

A)
B)
C)
D)
E)None of these

Question 23

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

Question 24

Select the curve by using the parametric equations to plot the points.

A)
B)
C)
D)
E)

Question 25

Select the curve by using the parametric equations to plot the points.

A)
B)
C)
D)
E)

Question 26

Match the parametric equations with the graphs labeled a-e.

A)
B)
C)
D)
E)

Question 27

Find the point(s) on the curve where the tangent is horizontal.

A)
B)
C)
D)
E)None of these

Question 28

Select the curve by using the parametric equations to plot the points.

A)
B)
C)
D)
E)

Question 29

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

Question 30

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