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Stewart - Calculus ET 8e Chapter 10 Form A
1. If a and b are fixed numbers, find parametric equations for the set of all points P determined as
shown in the figure, using the angle ang as the parameter. Write the equations for and
.
2. Find parametric equations for the path of a particle that moves once clockwise along the circle
, starting at .
4. Sketch the parametric curve and eliminate the parameter to find the Cartesian equation of the
curve.
6. Find an equation of the tangent to the curve at the point corresponding to the given value of the
parameter.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 10 Form A
7. Find an equation of the tangent to the curve at the point by first eliminating the parameter.
, ;
8. Set up an integral that represents the length of the curve. Then use your calculator to find the
length correct to four decimal places.
9. Find .
10. Set up, but do not evaluate, an integral that represents the length of the parametric curve.
If the parametric curve x f ( ), y g ( ) satisfies g '( ) 0, then it has a horizontal tangent when
.
12. Find an equation of the tangent to the curve at the point corresponding to the given value of the
parameter.
13. Find .
15. Find the area bounded by the curve and the line y = 2.5.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 10 Form A
16. Find the area of the region that lies inside both curves.
17. Using the arc length formula, set up, but do not evaluate, an integral equal to the total arc length of the
ellipse.
2 4 6 8 10 12 14
20. The point in a lunar orbit nearest the surface of the moon is called perilune and the point farthest
from the surface is called apolune. The Apollo 11 spacecraft was placed in an elliptical lunar orbit
with perilune altitude km and apolune altitude km (above the moon). Find an equation of
this ellipse if the radius of the moon is km and the center of the moon is at one focus.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 10 Form A
Answer Key
1.
2.
3.
4.
–5 –4 –3 –2 –1 1 2 3 4 5 x
–1
–2
–3
–4
–5
2
5. 2 y
7
6.
7.
8.
9.
10.
11.
True
12.
13.
14. False
15.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 10 Form A
16.
17.
6
18.
5
169
19.
4
20.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 10 Form B
3. Find an equation of the tangent to the curve at the point corresponding to the given value of the
parameter.
4. Find an equation of the tangent line to the curve at the point corresponding to the value of the
parameter.
, ;
5. True or False?
If the parametric curve x f ( ), y g ( ) satisfies g '( ) 0, then it has a horizontal tangent when
.
6. Find an equation of the tangent to the curve at the point corresponding to the given value of the
parameter.
7. A cow is tied to a silo with radius by a rope just long enough to reach the opposite side of the
silo. Find the area available for grazing by the cow. Round the answer to the nearest hundredth.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 10 Form B
8. Find .
9. True or False?
10. Find a Cartesian equation for the curve described by the given polar equation.
11. Find the area of the region that is bounded by the given curve and lies in the specified sector.
12. The point in a lunar orbit nearest the surface of the moon is called perilune and the point farthest
from the surface is called apolune. The Apollo 11 spacecraft was placed in an elliptical lunar orbit
with perilune altitude km and apolune altitude km (above the moon). Find an equation of
this ellipse if the radius of the moon is km and the center of the moon is at one focus.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 10 Form B
(a) Find the eccentricity and an equation of the directrix of the conic.
(b) Identify the conic.
(c) Sketch the curve.
(a) Find the eccentricity and an equation of the directrix of the conic.
(b) Identify the conic.
(c) Sketch the curve.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 10 Form B
Answer Key
1.
2
2. 2 y
7
3.
4.
5.
True
6.
7.
8.
9. False
10.
11.
12.
13. Vertices: (0, ± 5)
Foci: (0, ± 30 )
Asymptotes:
14. Vertex: (4, 1)
Focus: (9, 1)
Directrix: x = –1
15. Vertex: (0, 0)
1
Focus: ( , 0)
18
1
Directrix: x = –
18
16.
17.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 10 Form B
3
18. (a) eccentricity: , directrix:
5
(b) ellipse
(c)
1 2 3 4 5 r
13
19. (a) eccentricity: 4, directrix:
4
(b) hyperbola
(c)
1 2 3 4 5 r
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 10 Form B
7
20. (a) eccentricity: 1, directrix:
5
(b) parabola
(c)
1 2 3 4 5 r
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 10 Form C
a.
b.
c.
d.
e.
____ 2. Find the point(s) on the curve where the tangent is horizontal.
a.
b.
c.
d.
e. None of these
____ 3. Find the exact area of the surface obtained by rotating the given curve about the x-axis.
a.
b.
c.
d.
e. None of these
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 10 Form C
____ 4. Find a polar equation for the curve represented by the given Cartesian equation.
a.
b.
c.
d.
e.
____ 5. Find the point(s) of intersection of the curves and .
a.
b.
c.
d.
e.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 10 Form C
a.
b.
c.
d.
e. None of these
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 10 Form C
____ 7. The graph of the following curve is given. Find the area that it encloses.
4 8 12 16 20 24
a.
b. 81
A=
2
c.
d.
A=
e. 81
2
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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