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36. Performance Task Libby wants to graph a hyperbola with the equation y2 - x² + 16 = 0. The function y = √√x² - 16 represents part of the hyperbola. Libby used the TABLE feature on her graphing calculator to show several points on the graph of y=√x² - 16. X Y₁ 0 ERROR 1 ERROR 2 ERROR 3 ERROR 4 0 3 6 4.4721 X=0 Part A Explain why some entries show ERROR. Part B Using the information in the table, what can you conclude about the vertices of the equation y2-x2 + 16 = 0? Part C Write the equation y²-x² +16=0 in standard form to prove you correctly found the vertices from the table. 56 wo

36. Performance Task Libby wants to graph a hyperbola with the equation y2 - x² + 16 = 0. The function y = √√x² - 16 represents part of the hyperbola. Libby used the TABLE feature on her graphing calculator to show several points on the graph of y=√x² - 16. X Y₁ 0 ERROR 1 ERROR 2 ERROR 3 ERROR 4 0 3 6 4.4721 X=0 Part A Explain why some entries show ERROR. Part B Using the information in the table, what can you conclude about the vertices of the equation y2-x2 + 16 = 0? Part C Write the equation y²-x² +16=0 in standard form to prove you correctly found the vertices from the table. 56 wo

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter7: Conic Sections
Section: Chapter Questions
Problem 3CC
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PRACTICE & PROBLEM SOLVING Practice Mixed Review Available On APPLY ASSESSMENT PRACTICE 34. Write an equation of the hyperbola shown in 31. Model With Mathematics When the light from a lamp shines on a wall, a hyperbola is formed. What is the equation of the hyperbola with asymptotes y = ±3x? EX? the graph. G-GPE.1.3 I 81Y 20 -4-2 O 5 20 (0, 2) -4 35. SAT/ACT Which equation represents a hyperbola? 4x² +81y² + 12 = 0 B 9x² + 16y² - 4x - 24y + 18 = 0 Ⓒ49y² + 7y - 2x + 14 = 0 D-36x² - 36y² + 6x - 13y + 20 = 0 32. Model With Mathematics In order to take a panoramic photograph, a camera must have a hyperbolic mirror. The graphic shows that the camera is below the mirror. The lens is at one focus of the camera, and the mirror is at one vertex. Write an equation for the cross section of the mirror. Ⓡ 25x² - 121y² + 64 = 0 1 36. Performance Task Libby wants to graph a hyperbola with the equation y² - x² + 16 = 0. The function y = √x² - 16 represents part of the hyperbola. Libby used the TABLE feature on her graphing calculator to show several points on the graph of y = √√x² - 16. $ 1 (0, 2) 1 (0, -2.5) Y₁ ERROR 1 ERROR ERROR 3 ERROR 4 0 5 3 6 4.4721 X=0 **** Part A Explain why some entries show ERROR. Part B Using the information in the table, what can you conclude about the vertices of the equation y² - x² + 16 = 0? 33. Reason Jupiter's gravity changes a spacecraft's path to a hyperbola as it approaches. The focus of the hyperbola nearest the spacecraft's path is the center of Jupiter. The diameter of the planet is 139,822 km. Suppose the path of an approaching spacecraft has an equation with a = 80,000 km and c = 170,000 km. Assuming the transverse axis is horizontal, write the equation that models the path of the spacecraft as it approaches Jupiter. What is the distance from the spacecraft to the planet at the vertex of the hyperbola? Part C Write the equation y2 - x² +16=0 in standard form to prove you correctly found the vertices from the table. Go Online PearsonRealize.com 1 1 Хо N 2 ХА X Vo C C
Transcribed Image Text:PRACTICE & PROBLEM SOLVING Practice Mixed Review Available On APPLY ASSESSMENT PRACTICE 34. Write an equation of the hyperbola shown in 31. Model With Mathematics When the light from a lamp shines on a wall, a hyperbola is formed. What is the equation of the hyperbola with asymptotes y = ±3x? EX? the graph. G-GPE.1.3 I 81Y 20 -4-2 O 5 20 (0, 2) -4 35. SAT/ACT Which equation represents a hyperbola? 4x² +81y² + 12 = 0 B 9x² + 16y² - 4x - 24y + 18 = 0 Ⓒ49y² + 7y - 2x + 14 = 0 D-36x² - 36y² + 6x - 13y + 20 = 0 32. Model With Mathematics In order to take a panoramic photograph, a camera must have a hyperbolic mirror. The graphic shows that the camera is below the mirror. The lens is at one focus of the camera, and the mirror is at one vertex. Write an equation for the cross section of the mirror. Ⓡ 25x² - 121y² + 64 = 0 1 36. Performance Task Libby wants to graph a hyperbola with the equation y² - x² + 16 = 0. The function y = √x² - 16 represents part of the hyperbola. Libby used the TABLE feature on her graphing calculator to show several points on the graph of y = √√x² - 16. $ 1 (0, 2) 1 (0, -2.5) Y₁ ERROR 1 ERROR ERROR 3 ERROR 4 0 5 3 6 4.4721 X=0 **** Part A Explain why some entries show ERROR. Part B Using the information in the table, what can you conclude about the vertices of the equation y² - x² + 16 = 0? 33. Reason Jupiter's gravity changes a spacecraft's path to a hyperbola as it approaches. The focus of the hyperbola nearest the spacecraft's path is the center of Jupiter. The diameter of the planet is 139,822 km. Suppose the path of an approaching spacecraft has an equation with a = 80,000 km and c = 170,000 km. Assuming the transverse axis is horizontal, write the equation that models the path of the spacecraft as it approaches Jupiter. What is the distance from the spacecraft to the planet at the vertex of the hyperbola? Part C Write the equation y2 - x² +16=0 in standard form to prove you correctly found the vertices from the table. Go Online PearsonRealize.com 1 1 Хо N 2 ХА X Vo C C
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