EXERCISES
For more practice, see Extra Practice.
Practice and Problem Solving
A
Practice by Example
Examples 1, 2, and 3
(pages 535 and 536)
Graph each equation. Identify the conic section and describe the graph and its
lines of symmetry. Then find the domain and range.
1. 3y 2 - x 2 = 25
2. 2x 2 + y 2 = 36
3. x 2 + y 2 = 16
4. 3y 2 - x 2 = 9
5. 4x 2 + 25y 2 = 100
6. x 2 + y 2 = 49
7. x 2 - y 2 + 1 = 0
8. x 2 - 2y 2 = 4
9. 6x 2 + 6y 2 = 600
Example 4
(page 537)
10. x 2 + y 2 - 4 = 0
11. 6x 2 + 24y 2 - 96 = 0
12. 4x 2 + 4y 2 - 20 = 0
13. x 2 + 9y 2 = 1
14. 4x 2 - 36y 2 = 144
15. 4y2 - 36x2 = 1
16. 36x 2 + 4y 2 = 144
Identify the center and intercepts of each conic section. Give the domain and range
of each graph. On graphing calculator screens, each interval represents one unit.
y
17.
18.
1
⫺2
O
x
2
⫺1
19.
20.
y
2
⫺4
21.
y
2
⫺4 ⫺2
Example 5
(page 538)
B
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Apply Your Skills
O
⫺2
4
x
22.
O
4
x
Match each equation with a graph in Exercises 17–22.
23. x 2 - y 2 = 9
24. 4x 2 + 9y 2 = 36
25. y2 - x2 = 4
26. x 2 + 4y 2 = 64
27. 25x 2 + 9y 2 = 225
28. y2 - x2 = 9
Graph each equation. Describe the graph and its lines of symmetry. Then find the
domain and range.
29. 9x 2 - y 2 = 144
30. 11x 2 + 11y 2 = 44
31. -8x 2 + 32y 2 - 128 = 0
32. 25x 2 + 16y 2 - 320 = 0
Chapter 10 Quadratic Relations
33. a. Writing Describe the relationship between the center of a circle and the
axes of symmetry of the circle.
b. Make a Conjecture Where is the center of an ellipse or a hyperbola located
in relation to the axes of symmetry? Verify your conjectures with examples.
34. Light The light emitted from a lamp with a shade forms a shadow on the wall.
Explain how you could turn the lamp in relation to the wall so that the shadow
cast by the shade forms each conic section.
a. hyperbola
b. parabola
c. ellipse
d. circle
Mental Math Each given point is on the graph of the given equation. Use
symmetry to find at least one more point on the graph.
36. A 2!2, 1 B , x 2 + y 2 = 3
35. (2, -4), y 2 = 8x
37. A 2, 2!2 B , x 2 + 4y 2 = 36
38. (-2, 0), 9x 2 + 9y 2 - 36 = 0
39. A -3, 2!51 B , 6y 2 - 9x 2 - 225 = 0
40. A 0, !7 B , x 2 + 2y 2 = 14
Graph each circle so that the center is at the origin. Then write the equation.
41. radius 6
42. radius 12
43. diameter 8
44. diameter 2.5
45. Open-Ended Describe any other figures you can imagine that can be formed
by the intersection of a plane and other shapes.
C
Challenge
46. a. Graph the equation xy = 16. Use both positive and negative values for x.
b. Which conic section does the equation appear to model?
c. Identify any intercepts and lines of symmetry.
d. Does your graph represent a function? If so, rewrite the equation using
function notation.
47. The sharpened portion of the pencil at the right meets each painted side in a
curved path. Describe the curve and justify your reasoning.
48. An xy term has an interesting effect on the graph of a conic section. Sketch the
graph of each conic section below using your graphing calculator.
(Hint: To solve for y, you will need to complete a square.)
a. 4x 2 + 2xy + y 2 = 9
b. 4x 2 + 2xy - y 2 = 9
Reading Math
Cone comes from the
Indo-European word
for “sharpen.” Section
comes from the word
for “cut.”
49. Sound An airplane flying faster than the speed of sound creates a cone-shaped
pressure disturbance in the air. This is heard by people on the ground as a sonic
boom. What is the shape of the path on the ground?
Lesson 10-1 Exploring Conic Sections
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Standardized Test Prep
Multiple Choice
50. The graph of which equation of a circle contains all the points in the
table below?
x
y
-3
0
0 43
3
0
A. x 2 + y 2 - 4 = 0
C. x 2 + y 2 = 36
B. x 2 + y 2 = 25
D. 6x 2 + 6y 2 = 54
51. The graph of which ellipse contains all the points in the table below?
x
y
⫺4
⫺2
0
2
0 4兹3 42 4兹3
F. x 2 + 4y 2 = 16
H. 4x 2 + 25y 2 = 64
4
0
G. 4x 2 + 16y 2 = 144
I. 9x 2 + y 2 = 81
52. Which point is NOT on the graph of 4x 2 - y 2 = 4?
A. A -2, 22!3 B
B. (-1, 0)
C. (1, 0)
Take It to the NET
Online lesson quiz at
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Short Response
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D. (2, 2)
53. Which equation does NOT represent a line of symmetry for the
circle with equation x 2 + y 2 = 100?
G. y = 1
H. y = x
I. y = x + 1
2x
54. Which equation represents a line of symmetry for the ellipse with
equation x 2 + 9y 2 = 9?
A. y = -x
B. y = 0
C. y = x
D. xy = 1
F. x = 0
55. The graph of the equation x 2 + y 2 = 121 is a circle. Describe the graph
and its lines of symmetry. Find the domain and the range.
Chapter 10 Quadratic Relations
Mixed Review
Lesson 9-7
Lesson 9-1
Lesson 8-1
A standard number cube is tossed. Find each probability.
56. P(5 or greater than 3)
57. P(even or 6)
58. P(even or 7)
59. P(prime or 2)
Suppose z varies jointly with x and y. Write a function that models each
relationship. Find the value of z when x ≠ –2 and y ≠ 3.
60. z = -5 when x = -1 and y = -1
61. z = 72 when x = 3 and y = -6
62. z = 32 when x = 0.1 and y = 8
63. z = 5 when x = -4 and y = 2.5
Write an exponential equation y ≠ ab x whose graph passes through the
given points.
64. (-1, 2) and (3, 32)
67. Q 0, 13 R and (2, 3)
Lesson 6-8
65. Q 0, 12 R and (2, 8)
68. Q-1, 23 R and (2, 18)
66. (1, 6) and (2, 12)
69. Q -1, 18 R and (4, 4)
Expand each binomial.
70. (x - y)3
71. (p + q)6
72. (x - 2)4
73. (3 - x)5
Lesson 10-1 Exploring Conic Sections
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