Deck 9: Parametric Equations and Polar Coordinates

Question 1

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

A)
B)
C)
D)
E)

Answer 1

Question 2

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)

Answer 2

Question 3

Find the area that the curve encloses.

Answer 3

Question 4

Find the eccentricity of the conic.

A)
B)
C)
D)
E)

Question 5

The planet Mercury travels in an elliptical orbit with eccentricity 0.403 .Its minimum distance from the Sun is km.If the perihelion distance from a planet to the Sun is a (1- e) and the aphelion distance is a (1+e) ,find the maximum distance (in km)from Mercury to the Sun.

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

Question 6

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 7

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

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

Question 8

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

A)
B)
C)
D)
E)

Question 9

The orbit of Hale-Bopp comet,discovered in 1995,is an ellipse with eccentricity 0.995 and one focus at the Sun.The length of its major axis is 369.9 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 a(1-e) and the aphelion distance is a(1+e) .Find the answer in AU and round to the nearest hundredth.

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

Question 10

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

A)
B)
C)
D)
E)

Question 11

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 12

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

A)
B)
C)
D)
E)

Question 13

Sketch the polar curve with the given equation.

A)
B)
C)
D)

Question 14

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

Question 15

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

A) ,ellipse
B) ,ellipse
C) ,hyperbola
D) ,hyperbola

Question 16

Find the length of the polar curve.

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

Question 17

Find the area enclosed by the curve .

Question 18

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 19

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 20

Find the Cartesian coordinates of the point .

A)
B)
C)
D)
E)

Question 21

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

A)
B)
C)
D)
E)

Question 22

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

A)
B)
C)
D)
E)

Question 23

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

A)
B)
C)
D)
E)

Question 24

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 25

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

A)
B)
C)
D)
E)

Question 26

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

Question 27

Find the length of the curve. , ,

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

Question 28

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

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

Question 29

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

Question 30

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

A)
B)
C)
D)
E)