Stewart - Calculus ET 8e Chapter 10. All Answers

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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 . 3. Eliminate the parameter to find a Cartesian equation of the curve. 4. Sketch the parametric curve and eliminate the parameter to find the Cartesian equation of the curve. 5. Eliminate the parameter to find a 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.Stewart - Calculus ET 8e Chapter 10 Form A © 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. 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. 11. True or False? 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 . 14. True or False? The exact length of the parametric curve is . 15. Find the area bounded by the curve and the line y = 2.5.Stewart - Calculus ET 8e Chapter 10 Form A © 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. 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. 18. Find the area enclosed by the curve . 19. Find the area that the curve encloses. 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.Stewart - Calculus ET 8e Chapter 10 Form A © 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. Answer Key 1. 2. 3. 4. –5 –4 –3 –2 –1 1 2 3 4 5 x 5 4 3 2 1 –1 –2 –3 –4 –5 y 5. 2 2 7 y 6. 7. 8. 9. 10. 11. True 12. 13. 14. False 15.Stewart - Calculus ET 8e Chapter 10 Form A © 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. 16. 17. 18. 6 5 19. 169 4 20.Stewart - Calculus ET 8e Chapter 10 Form B © 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. 1. Eliminate the parameter to find a Cartesian equation of the curve. 2. Eliminate the parameter to find a Cartesian equation of the curve. 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.Stewart - Calculus ET 8e Chapter 10 Form B © 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. 8. Find . 9. True or False? The exact length of the parametric curve is . 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. 13. Find the vertices, foci, and asymptotes of the hyperbola. 14. Find the vertex, focus, and directrix of the parabola. 15. Find the vertex, focus, and directrix fo the parabola. 16. Find an equation of the conic satisfying the given conditions. Hyperbola, foci (5, 6) and (5, –4), asymptotes x = 2y + 3 and x = – 2y + 7 17. Find an equation of the conic satisfying the given conditions. Hyperbola, foci (5, 6) and (5, –2), asymptotes x = 2y + 1 and x = – 2y + 9Stewart - Calculus ET 8e Chapter 10 Form B © 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. 18. 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. 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. 20. 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.Stewart - Calculus ET 8e Chapter 10 Form B © 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. Answer Key 1. 2. 2 2 7 y 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) Focus: ( 1 18 , 0) Directrix: x = – 1 18 16. 17.Stewart - Calculus ET 8e Chapter 10 Form B © 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. 18. (a) eccentricity: 3 5 , directrix: (b) ellipse (c) 1 2 3 4 5 r 19. (a) eccentricity: 4, directrix: 13 4 (b) hyperbola (c) 1 2 3 4 5 rStewart - Calculus ET 8e Chapter 10 Form B © 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. 20. (a) eccentricity: 1, directrix: 7 5 (b) parabola (c) 1 2 3 4 5 rStewart – Calculus ET 8e Chapter 10 Form C © 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. Select the correct answer for each question. ____ 1. Find parametric equations to represent the line segment from . 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 theseStewart – Calculus ET 8e Chapter 10 Form C © 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. ____ 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.Stewart – Calculus ET 8e Chapter 10 Form C © 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. ____ 6. Find the length of the polar curve. a. b. c. d. e. None of theseStewart – Calculus ET 8e Chapter 10 Form C © 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. ____ 7. The graph of the following curve is given. Find the area that it encloses. 4 8 12 16 20 24 a. b. A = 81 2 c. d. A = e. 81 2Stewart – Calculus ET 8e Chapter 10 Form C © 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. ____ 8. Find an equation for the conic that satisfies the given conditions. hyperbola, foci (0, ± ) , vertices (0, ± ) a. b. c. d. e. ____ 9. Find an equation of the hyperbola centered at the origin that satisfies the given condition. Vertices: (± 4, 0), asymptotes: y = ± 7 4 x a. b. c. d.Stewart – Calculus ET 8e Chapter 10 Form C © 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. ____ 10. Find an equation of the ellipse that satisfies the given conditions. Foci: (0, ± 8), vertices (0, ± 9) a. b. c. d. ____ 11. Write a polar equation in r and of an ellipse with the focus at the origin, with the eccentricity and directrix . a. b. c. d. e.Stewart – Calculus ET 8e Chapter 10 Form C © 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. ____ 12. The orbit of Hale-Bopp comet, discovered in 1995, is an ellipse with eccentricity and one focus at the Sun. The length of its major axis is 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 and the aphelion distance is .) Find the answer in AU and round to the nearest hundredth. a. AU b. AU c. AU d. AU e. AU ____ 13. Write a polar equation of the conic that has a focus at the origin, eccentricity 7 2 , and directrix . Identify the conic. a. , hyperbola b. , hyperbola c. , ellipse d. , ellipse ____ 14. Suppose a planet is discovered that revolves around its sun in an elliptical orbit with the sun at one focus. Its perihelion distance (minimum distance from the planet to the sun) is approximately 2.3 km, and its aphelion distance (maximum distance from the planet to the sun) is approximately 2.7 km. Approximate the eccentricity of the planet’s orbit. Round to three decimal places. a. 1.174 b. 12.5 c. 0.08 d. 0.852Stewart – Calculus ET 8e Chapter 10 Form C © 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. ____ 15. The planet Mercury travels in an elliptical orbit with eccentricity . Its minimum distance from the Sun is km. If the perihelion distance from a planet to the Sun is and the aphelion distance is , find the maximum distance (in km) from Mercury to the Sun. a. km b. km c. km d. km e. km ____ 16. 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.Stewart – Calculus ET 8e Chapter 10 Form C © 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. ____ 17. Find the eccentricity of the conic. a. b. c. d. e. ____ 18. Use a graph to estimate the values of for which the curves and intersect. Round your answer to two decimal places. a. b. c. d. e.Stewart – Calculus ET 8e Chapter 10 Form C © 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. ____ 19. A cross-section of a parabolic reflector is shown in the figure. The bulb is located at the focus and the opening at the focus is 18 cm. Find an equation of the parabola. Let V be the origin. Find the diameter of the opening |CD| , 19 cm from the vertex. a. b. c. The equation is d. e. The equation is f. The equation isStewart – Calculus ET 8e Chapter 10 Form C © 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. ____ 20. Find the vertices, foci and asymptotes of the hyperbola. a. The foci are b. The vertices are (4 5 , 5) c. The foci are d. The vertices are e. The asymptote is f. The asymptotes areStewart – Calculus ET 8e Chapter 10 Form C © 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. Answer Key 1. D 2. D 3. A 4. A 5. C 6. D 7. B 8. E 9. A 10. A 11. A 12. C 13. B 14. C 15. A 16. B 17. C 18. B, E 19. A, B 20. B, CStewart – Calculus ET 8e Chapter 10 Form D © 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. Select the correct answer for each question. ____ 1. Find parametric equations to represent the line segment from . a. b. c. d. e. ____ 2. The curve cross itself at some point . Find the equations of both tangent lines at that point. a. b. c. d. e.Stewart – Calculus ET 8e Chapter 10 Form D © 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. ____ 3. Find the surface area generated by rotating the lemniscate about the line . a. b. c. d. e. ____ 4. In the LORAN (LOng RAnge Navigation) radio navigation system, two radio stations located at A and B transmit simultaneous signals to a ship or an aircraft located at P. The onboard computer converts the time difference in receiving these signals into a distance difference , and this, according to the definition of a hyperbola, locates the ship or aircraft on one branch of a hyperbola (see the figure). Suppose that station B is located L = mi due east of station A on a coastline. A ship received the signal from B microseconds (µs) before it received the signal from A. Assuming that radio signals travel at a speed of ft /µs and if the ship is due north of B, how far off the coastline is the ship? Round your answer to the nearest mile. a. miles b. miles c. miles d. miles e. milesStewart – Calculus ET 8e Chapter 10 Form D © 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. ____ 5. Suppose a planet is discovered that revolves around its sun in an elliptical orbit with the sun at one focus. Its perihelion distance (minimum distance from the planet to the sun) is approximately 2.3 km, and its aphelion distance (maximum distance from the planet to the sun) is approximately 2.7 km. Approximate the eccentricity of the planet’s orbit. Round to three decimal places. a. 1.174 b. 12.5 c. 0.08 d. 0.852 ____ 6. If a projectile is fired with an initial velocity of meters per second at an angle above the horizontal and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equations , , where g is the acceleration of gravity . If a gun is fired with and when will the bullet hit the ground? a. b. c. d. e.Stewart – Calculus ET 8e Chapter 10 Form D © 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. ____ 7. Describe the motion of a particle with position as t varies in the given interval . a. Moves once counterclockwise along the circle starting and ending at . b. Moves once counterclockwise along the ellipse starting and ending at . c. Moves once counterclockwise along the ellipse starting and ending at . d. Moves once clockwise along the ellipse starting and ending at . e. Moves once clockwise along the circle starting and ending at . ____ 8. Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. a. b. c. d. e. None of theseStewart – Calculus ET 8e Chapter 10 Form D © 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. ____ 9. 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 ____ 10. Find a polar equation for the curve represented by the given Cartesian equation. a. b. c. d. e.Stewart – Calculus ET 8e Chapter 10 Form D © 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. ____ 11. Find the polar equation for the curve represented by the given Cartesian equation. a. b. c. d. e.Stewart – Calculus ET 8e Chapter 10 Form D © 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. ____ 12. Sketch the polar curve with the given equation. a. 1 c. 1 2 3 4 5 6 b. 1 2 3 4 5 6 d. 1Stewart – Calculus ET 8e Chapter 10 Form D © 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. ____ 13. Find the length of the polar curve. a. b. c. d. e. None of these ____ 14. Find the area of the region enclosed by one loop of the curve. a. b. c. d. e.Stewart – Calculus ET 8e Chapter 10 Form D © 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. ____ 15. Find the area of the region that lies inside the first curve and outside the second curve. a. b. c. d. e. ____ 16. Find an equation of the parabola with focus and directrix . a. b. c. d. e.Stewart – Calculus ET 8e Chapter 10 Form D © 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. ____ 17. Find an equation for the conic that satisfies the given conditions. ellipse, foci , length of major axis 8 a. b. c. d. e. ____ 18. Write a polar equation in r and of an ellipse with the focus at the origin, with the eccentricity and directrix . a. b. c. d. e.Stewart – Calculus ET 8e Chapter 10 Form D © 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. ____ 19. The orbit of Hale-Bopp comet, discovered in 1995, is an ellipse with eccentricity and one focus at the Sun. The length of its major axis is 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 and the aphelion distance is .) Find the answer in AU and round to the nearest hundredth. a. AU b. AU c. AU d. AU e. AU ____ 20. Write a polar equation in r and of an ellipse with the focus at the origin, with the eccentricity and vertex at . a. b. c. d. e.Stewart – Calculus ET 8e Chapter 10 Form D © 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. Answer Key 1. D 2. D 3. B 4. D 5. C 6. B 7. D 8. D 9. A 10. A 11. C 12. A 13. D 14. B 15. B 16. E 17. B 18. A 19. C 20. DStewart – Calculus ET 8e Chapter 10 Form 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. ____ 1. Find parametric equations to represent the line segment from . Select the correct answer. a. b. c. d. e. 2. Describe the motion of a particle with position as t varies in the given interval . 3. Find the point(s) on the curve where the tangent is horizontal. 4. Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. ____ 5. Find a polar equation for the curve represented by the given Cartesian equation. Select the correct answer. a. b. c. d. e. 6. Find the slope of the tangent line to the given polar curve at the point specified by the value of . 7. Find the area of the region that lies inside the first curve and outside the second curve.Stewart – Calculus ET 8e Chapter 10 Form 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. 8. Graph of the following curve is given. Find its length. 1 2 3 4 5 6 r 9. The graph of the following curve is given. Find the area that it encloses. 4 8 12 16 20 24Stewart – Calculus ET 8e Chapter 10 Form 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. ____ 10. Find an equation for the conic that satisfies the given conditions. Select the correct answer. parabola, vertex (0, 0), focus (0, – ) a. b. c. d. e. 11. Find an equation for the conic that satisfies the given conditions. hyperbola, foci (0, ± ) , vertices (0, ± ) 12. Find an equation of the hyperbola centered at the origin that satisfies the given condition. Vertices: (± 4, 0), asymptotes: y = ± 7 4 x 13. Find an equation of the hyperbola with vertices and asymptotes . 14. Find an equation for the conic that satisfies the given conditions. ellipse, foci , length of major axis 8Stewart – Calculus ET 8e Chapter 10 Form 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. ____ 15. In the LORAN (LOng RAnge Navigation) radio navigation system, two radio stations located at A and B transmit simultaneous signals to a ship or an aircraft located at P. The onboard computer converts the time difference in receiving these signals into a distance difference , and this, according to the definition of a hyperbola, locates the ship or aircraft on one branch of a hyperbola (see the figure). Suppose that station B is located L = mi due east of station A on a coastline. A ship received the signal from B microseconds (µs) before it received the signal from A. Assuming that radio signals travel at a speed of ft /µs and if the ship is due north of B, how far off the coastline is the ship? Round your answer to the nearest mile. Select the correct answer. a. miles b. miles c. miles d. miles e. miles 16. Find an equation of the ellipse that satisfies the given conditions. Foci: (0, ± 1), vertices (0, ± 6) 17. The orbit of Hale-Bopp comet, discovered in 1995, is an ellipse with eccentricity and one focus at the Sun. The length of its major axis is 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 and the aphelion distance is .) Find the answer in AU and round to the nearest hundredth. 18. Write a polar equation of the conic that has a focus at the origin, eccentricity 7 2 , and directrix . Identify the conic.Stewart – Calculus ET 8e Chapter 10 Form 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. ____ 19. Find the equation of the directrix of the conic. Select the correct answer. a. b. c. d. e. 20. The planet Mercury travels in an elliptical orbit with eccentricity . Its minimum distance from the Sun is km. If the perihelion distance from a planet to the Sun is and the aphelion distance is , find the maximum distance (in km) from Mercury to the Sun.Stewart – Calculus ET 8e Chapter 10 Form 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. Answer Key 1. D 2. Moves once clockwise along the ellipse starting and ending at . 3. 4. 5. A 6. 7. 8. L 24 9. A = 81 2 10. D 11. 12. 13. 14. 15. D 16. 17. AU 18. , hyperbola 19. E 20. kmStewart – Calculus ET 8e Chapter 10 Form F © 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. 1. Find parametric equations to represent the line segment from . Select the correct answer. a. b. c. d. e. 2. If a projectile is fired with an initial velocity of meters per second at an angle above the horizontal and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equations , , where g is the acceleration of gravity . If a gun is fired with and when will the bullet hit the ground? 3. Describe the motion of a particle with position as t varies in the given interval . 4. Find the point(s) on the curve where the tangent is horizontal. Select the correct answer. a. b. c. d. e. None of theseStewart – Calculus ET 8e Chapter 10 Form F © 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. 5. Find the length of the curve. Select the correct answer. , , a. b. c. d. e. None of these 6. Find the exact area of the surface obtained by rotating the given curve about the x-axis. 7. Find the point(s) of intersection of the curves and . 8. Find the surface area generated by rotating the lemniscate about the line . 9. Find the area of the region enclosed by one loop of the curve. Select the correct answer. a. b. c. d. e.Stewart – Calculus ET 8e Chapter 10 Form F © 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. 10. Graph of the following curve is given. Find its length. Select the correct answer. 1 2 3 4 5 6 r a. L 25 b. L 24 c. L 26 d. L 32 e. L 20 11. Find an equation for the conic that satisfies the given conditions. parabola, vertex (0, 0), focus (0, – ) 12. Find an equation of the parabola with focus and directrix . 13. Find an equation of the hyperbola with vertices and asymptotes .Stewart – Calculus ET 8e Chapter 10 Form F © 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. 14. In the LORAN (LOng RAnge Navigation) radio navigation system, two radio stations located at A and B transmit simultaneous signals to a ship or an aircraft located at P. The onboard computer converts the time difference in receiving these signals into a distance difference , and this, according to the definition of a hyperbola, locates the ship or aircraft on one branch of a hyperbola (see the figure). Suppose that station B is located L = mi due east of station A on a coastline. A ship received the signal from B microseconds (µs) before it received the signal from A. Assuming that radio signals travel at a speed of ft /µs and if the ship is due north of B, how far off the coastline is the ship? Round your answer to the nearest mile. Select the correct answer. a. miles b. miles c. miles d. miles e. miles 15. Match the equation with the correct graph. 16. Find an equation of the ellipse that satisfies the given conditions. Foci: (0, ± 8), vertices (0, ± 9) 17. Write a polar equation in r and of an ellipse with the focus at the origin, with the eccentricity and directrix .Stewart – Calculus ET 8e Chapter 10 Form F © 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. 18. Write a polar equation in r and of an ellipse with the focus at the origin, with the eccentricity and vertex at . 19. The planet Mercury travels in an elliptical orbit with eccentricity . Its minimum distance from the Sun is km. If the perihelion distance from a planet to the Sun is and the aphelion distance is , find the maximum distance (in km) from Mercury to the Sun. Select the correct answer. a. km b. km c. km d. km e. km 20. Write a polar equation in r and of a hyperbola with the focus at the origin, with the eccentricity and directrix .Stewart – Calculus ET 8e Chapter 10 Form F © 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. Answer Key 1. D 2. 3. Moves once clockwise along the ellipse starting and ending at . 4. D 5. D 6. 7. 8. 9. B 10. B 11. 12. 13. 14. D 15. –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 x 87654321 –1 –2 –3 –4 –5 –6 –7 –8 y 16. 17.Stewart – Calculus ET 8e Chapter 10 Form F © 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. 18. 19. A 20.Stewart - Calculus ET 8e Chapter 10 Form G © 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. 1. Find parametric equations to represent the line segment from . ____ 2. Find the point(s) on the curve where the tangent is horizontal. Select the correct answer. 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. 4. Find a polar equation for the curve represented by the given Cartesian equation. 5. Find the point(s) of intersection of the curves and . 6. Find the surface area generated by rotating the lemniscate about the line . ____ 7. Find the area of the region that lies inside the first curve and outside the second curve. Select the correct answer. a. b. c. d. e.Stewart - Calculus ET 8e Chapter 10 Form G © 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. 8. The graph of the following curve is given. Find the area that it encloses. 4 8 12 16 20 24 9. Find an equation of the hyperbola centered at the origin that satisfies the given condition. Vertices: (± 4, 0), asymptotes: y = ± 7 4 x 10. Find an equation of the hyperbola with vertices and asymptotes . ____ 11. Find an equation for the conic that satisfies the given conditions. Select the correct answer. ellipse, foci , length of major axis 8 a. b. c. d. e.Stewart - Calculus ET 8e Chapter 10 Form G © 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. ____ 12. In the LORAN (LOng RAnge Navigation) radio navigation system, two radio stations located at A and B transmit simultaneous signals to a ship or an aircraft located at P. The onboard computer converts the time difference in receiving these signals into a distance difference , and this, according to the definition of a hyperbola, locates the ship or aircraft on one branch of a hyperbola (see the figure). Suppose that station B is located L = mi due east of station A on a coastline. A ship received the signal from B microseconds (µs) before it received the signal from A. Assuming that radio signals travel at a speed of ft /µs and if the ship is due north of B, how far off the coastline is the ship? Round your answer to the nearest mile. Select the correct answer. a. miles b. miles c. miles d. miles e. miles 13. Match the equation with the correct graph. 14. Find an equation of the ellipse that satisfies the given conditions. Foci: (0, ± 1), vertices (0, ± 6) 15. Find an equation of the ellipse that satisfies the given conditions. Foci: (0, ± 8), vertices (0, ± 9) 16. Write a polar equation in r and of an ellipse with the focus at the origin, with the eccentricity and directrix .Stewart - Calculus ET 8e Chapter 10 Form G © 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. 17. The orbit of Hale-Bopp comet, discovered in 1995, is an ellipse with eccentricity and one focus at the Sun. The length of its major axis is 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 and the aphelion distance is .) Find the answer in AU and round to the nearest hundredth. 18. Find the equation of the directrix of the conic. 19. Write a polar equation in r and of a hyperbola with the focus at the origin, with the eccentricity and directrix . ____ 20. Find the eccentricity of the conic. Select the correct answer. a. b. c. d. e.Stewart - Calculus ET 8e Chapter 10 Form G © 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. Answer Key 1. 2. D 3. 4. 5. 6. 7. B 8. A = 81 2 9. 10. 11. B 12. D 13. –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 x 87654321 –1 –2 –3 –4 –5 –6 –7 –8 y 14. 15.Stewart - Calculus ET 8e Chapter 10 Form G © 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. 16. 17. AU 18. 19. 20. CStewart - Calculus ET 8e Chapter 10 Form H © 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. 1. Find parametric equations to represent the line segment from . 2. Find the point(s) on the curve where the tangent is horizontal. ____ 3. Find the length of the curve. Select the correct answer. , , a. b. c. d. e. None of these 4. Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. 5. Find the exact area of the surface obtained by rotating the given curve about the x-axis. 6. The curve cross itself at some point . Find the equations of both tangent lines at that point.Stewart - Calculus ET 8e Chapter 10 Form H © 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. ____ 7. Find the polar equation for the curve represented by the given Cartesian equation. Select the correct answer. a. b. c. d. e. 8. Find the length of the polar curve. 9. Find the surface area generated by rotating the lemniscate about the line . 10. Find the area of the region that lies inside the first curve and outside the second curve.Stewart - Calculus ET 8e Chapter 10 Form H © 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. ____ 11. Graph of the following curve is given. Find its length. Select the correct answer. 1 2 3 4 5 6 r a. L 25 b. L 24 c. L 26 d. L 32 e. L 20 12. Find an equation of the parabola with focus and directrix . 13. Find an equation of the hyperbola with vertices and asymptotes . 14. Write a polar equation in r and of an ellipse with the focus at the origin, with the eccentricity and directrix . 15. The orbit of Hale-Bopp comet, discovered in 1995, is an ellipse with eccentricity and one focus at the Sun. The length of its major axis is 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 and the aphelion distance is .) Find the answer in AU and round to the nearest hundredth.Stewart - Calculus ET 8e Chapter 10 Form H © 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. 16. Write a polar equation of the conic that has a focus at the origin, eccentricity 7 2 , and directrix . Identify the conic. 17. Suppose a planet is discovered that revolves around its sun in an elliptical orbit with the sun at one focus. Its perihelion distance (minimum distance from the planet to the sun) is approximately 2.3 km, and its aphelion distance (maximum distance from the planet to the sun) is approximately 2.7 km. Approximate the eccentricity of the planet’s orbit. Round to three decimal places. ____ 18. The planet Mercury travels in an elliptical orbit with eccentricity . Its minimum distance from the Sun is km. If the perihelion distance from a planet to the Sun is and the aphelion distance is , find the maximum distance (in km) from Mercury to the Sun. Select the correct answer. a. km b. km c. km d. km e. km 19. Write a polar equation in r and of a hyperbola with the focus at the origin, with the eccentricity and directrix . ____ 20. Find the eccentricity of the conic. Select the correct answer. a. b. c. d. e.Stewart - Calculus ET 8e Chapter 10 Form H © 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. Answer Key 1. 2. 3. D 4. 5. 6. 7. C 8. 9. 10. 11. B 12. 13. 14. 15. AU 16. , hyperbola 17. 0.08 18. A 19. 20. C [Show More]

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