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
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
36 please
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e05d8d1-3997-4023-8636-4176c027f4f7%2F13439384-5c3a-414b-8504-d50447ffca82%2Fym1ad9l_processed.jpeg&w=3840&q=75)
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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