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661 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
10.5 Area and Arc Length in Polar Coordinates
Answer Section
10.6 Polar Equations of Conics and Kepler’s Laws
662
10.6 Polar Equations of Conics and Kepler’s Laws
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1.
Identify the conic for the polar equation
when
.
a.
hyperbola
b.
ellipse
c.
parabola
____ 2. Identify the graph for the polar equation .
a. d.
b. e.
663 Chapter 10: Conics, Parametric Equations, and Polar Coordinates c.
____ 3. Identify the graph for the polar equation .
a. d.
b. e.
10.6 Polar Equations of Conics and Kepler’s Laws
664
c.
____ 4. Identify the graph for the polar equation .
a. d.
b. e.
665 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
c.
____ 5. Find the eccentricity and distance from the pole to the directrix of the conic. Then sketch
and identify the graph. Use a graphing utility to confirm your results.
eccentricity:
distance from pole to directrix:
The graph is an ellipse.
eccentricity: 3
distance from pole to directrix:
The graph is a hyperbola.
10.6 Polar Equations of Conics and Kepler’s Laws
666
b. eccentricity: 3
e. eccentricity: 3
distance from pole to directrix:
distance from pole to directrix:
The graph is an ellipse.
The graph is a hyperbola.
eccentricity:
distance from pole to directrix:
The graph is an ellipse.
____ 6. Find the eccentricity of the polar equation .
78
26
13
667 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
____ 7. Find the distance from the pole to the directrix for the conic .
14
42
7
____ 8. Find the eccentricity and distance from the pole to the directrix of the conic. Then sketch
and identify the graph. Use a graphing utility to confirm your results.
a. eccentricity: d. eccentricity:
distance from pole to directrix: distance from pole to directrix:
The graph is an ellipse. The graph is an ellipse.
10.6 Polar Equations of Conics and Kepler’s Laws
668
eccentricity:
distance from pole to directrix:
The graph is a hyperbola.
eccentricity:
distance from pole to directrix:
The graph is a hyperbola.
eccentricity:
distance from pole to directrix:
The graph is an ellipse.
____ 9. Find the eccentricity of the polar equation .
28
14
d.
e. 7
669 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
____ 10. Find the distance from the pole to the directrix for the conic .
32
16
8
____
11.
Find the eccentricity of the polar equation
.
a.
b.
c.
d.
e.
____
12.
Find the distance from the pole to the directrix for the conic
.
a.
b.
c.
30
d.
e.
62
____
13.
Find a polar equation for the parabola with its focus at the pole, eccentricity e = 1,
and directrix
.
a.
b.
c.
d.
e.
10.6 Polar Equations of Conics and Kepler’s Laws
670
____
14.
Find a polar equation for the ellipse with its focus at the pole, eccentricity
, and
directrix
.
a.
b.
c.
d.
e.
____
15.
Find a polar equation for the hyperbola with its focus at the pole, eccentricity
,
and directrix
.
a.
b.
c.
d.
e.
____
16.
Find a polar equation for the parabola with its focus at the pole and vertex
.
a.
b.
c.
d.
e.
671 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
____ 17. Find a polar equation for the ellipse with its focus at the pole and vertices
.
a.
b.
c.
d.
e.
____ 18. Find a polar equation for the hyperbola with its focus at the pole and vertices
.
a.
b.
c.
d.
e.
____ 19.
Pluto moves in an elliptical orbit with the sun at one of the foci. The length of half of
the major axis is
kilometers, and the eccentricity is 0.2488. Find the perihelion distance
of Pluto from the sun. Round your answer to the nearest kilometers.
7,375,412,800 kilometers
4,436,587,201 kilometers
4,436,587,200 kilometers
8,873,174,399 kilometers
8,873,174,401 kilometers
10.6 Polar Equations of Conics and Kepler’s Laws
672
10.6 Polar Equations of Conics and Kepler’s Laws
Answer Section
