10.6 Polar Equations of Conics and Kepler’s Laws 635
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.
636 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 637
c.
____ 4. Identify the graph for the polar equation .
a. d.
b. e.
638 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.
a. eccentricity:
distance from pole to directrix:
The graph is an ellipse.
d. eccentricity: 3
distance from pole to directrix:
The graph is a hyperbola.
10.6 Polar Equations of Conics and Kepler’s Laws 639
b. eccentricity: 3
distance from pole to directrix:
The graph is an ellipse.
e. eccentricity: 3
distance from pole to directrix:
The graph is a hyperbola.
c. eccentricity:
distance from pole to directrix:
The graph is an ellipse.
____ 6. Find the eccentricity of the polar equation .
a. 78
b.
c. 26
d. 13
e.
640 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
____ 7. Find the distance from the pole to the directrix for the conic .
a.
b. 14
c.
d. 42
e. 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:
distance from pole to directrix:
The graph is an ellipse.
d. eccentricity:
distance from pole to directrix:
The graph is an ellipse.
10.6 Polar Equations of Conics and Kepler’s Laws 641
b. eccentricity:
distance from pole to directrix:
The graph is a hyperbola.
e. eccentricity:
distance from pole to directrix:
The graph is an ellipse.
c. eccentricity:
distance from pole to directrix:
The graph is a hyperbola.
____ 9. Find the eccentricity of the polar equation .
a. 28
b. 14
c.
d.
e. 7
642 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
____ 10. Find the distance from the pole to the directrix for the conic .
a.
b. 32
c. 16
d.
e. 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 643
____ 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.
644 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.
a. 7,375,412,800 kilometers
b. 4,436,587,201 kilometers
c. 4,436,587,200 kilometers
d. 8,873,174,399 kilometers
e. 8,873,174,401 kilometers
10.6 Polar Equations of Conics and Kepler’s Laws 645
10.6 Polar Equations of Conics and Kepler’s Laws
Answer Section