Larson_Calculus_10e ch10sec06
MULTIPLE CHOICE
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.
c.
3. Identify the graph for the polar equation .
a.
d.
b.
e.
c.
4. Identify the graph for the polar equation .
a.
d.
b.
e.
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.
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.
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.
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
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.
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.
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