Chapter 10
Homework
1
Lesson 10-1
pages 538–541 Exercises
2.
1.
Hyperbola: center (0, 0),
y-intercepts at ± 5 3 , no
3
x-intercepts, the lines of
symmetry are the x- and
y-axes; domain: all real
numbers, range: y >
–
5 3
or y <
.
–
5
Ellipse: center (0, 0), x-intercepts at ±3 2,
y-intercepts at ±6, the lines of symmetry
are the x- and y-axes; domain:
–3 2<
–x <
– 3 2, range –6 <
–y <
– 6.
3
3
3
10-1
2
Lesson 10-1
3.
5.
Circle: center (0, 0), radius 4,
x-intercepts at ±4, y-intercepts
at ±4, there are infinitely many
lines of symmetry; domain:
–4 <
–x <
– 4, range: –4 <
–y<
– 4.
Ellipse: center (0, 0), y-intercepts
at ±2, x-intercepts at ±5, the lines
of symmetry are the x- and y-axes;
domain: –5 <
–x <
– 5, range: –2 <
–y <
– 2.
6.
4.
Hyperbola: center (0, 0), y-intercepts
at ± 3, no x-intercepts, the lines of
symmetry are the x- and y-axes; domain:
all real numbers, range: y <
– 3 or y >
– 3.
Circle: center (0, 0), radius 7, x- and
y-intercepts at ±7, there are infinitely
many lines of symmetry; domain:
–7 <
–x <
– 7, range: –7 <
–y <
– 7.
3
Lesson 10-1
7.
9.
Hyperbola: center (0, 0), y-intercepts
at ±1, the lines of symmetry are the
x- and y-axes; domain: all real numbers,
range: y <
– –1 or y >
– 1.
8.
Circle: center (0, 0), radius 10, x- and
y-intercepts at ±10, there are infinitely
many lines of symmetry; domain:
–10 <
–x <
– 10, range: –10 <
–y <
– 10.
10.
Hyperbola: center (0, 0), x-intercepts
at ±2, the lines of symmetry are the
x- and y-axes; domain: x <
– –2 or x >
– 2,
range: all real numbers.
10-1
Circle: center (0, 0), radius 2, x- and
y-intercepts at ±2, there are infinitely
many lines of symmetry; domain:
–2 <
–x <
– 2, range: –2 <
–y<
– 2.
4
Lesson 10-1
11.
13.
Ellipse: center (0, 0), x-intercepts
at ±4, y-intercepts at ±2, the lines
of symmetry are the x- and y-axes;
domain: –4 <
– x<
– 4, range: –2 <
– y<
– 2.
Ellipse: center (0, 0), x-intercepts at ±1,
y-intercepts at ± 1 , the lines of symmetry
3
are the x- and y-axes; domain:
12.
1 y 1.
–1 <
–x <
– 1, range: 3 <
– <
–3
Circle: center (0, 0), radius 5, xand y-intercepts at ± 5, there are
infinitely many lines of symmetry;
domain: – 5 <
–x<
– 5,
range: – 5 <
–y <
– 5.
10-1
5
Lesson 10-1
16.
14.
Hyperbola: center (0, 0), x-intercepts
at ±6, the lines of symmetry are the
x- and y-axes; domain: x <
– –6 or x >
– 6,
range: all real numbers.
15.
Ellipse: center (0, 0), x-intercepts
at ±2, y-intercepts at ±6, the lines of
symmetry are the x- and y-axes;
domain: –2 <
–x <
– 2, range: –6 <
–y <
– 6.
17. center (0, 0), x-intercepts at ±3,
y-intercepts at ±2; domain: –3 <
–x <
– 3,
range: –2 <
–y <
–2
Hyperbola: center (0, 0), y-intercepts at ±
1
,
2
the lines of symmetry are the x- and y-axes;
1
1
domain: all real numbers, range: y <
– – or y >
– .
2
10-1
2
6
Lesson 10-1
18. center (0, 0), no x-intercepts,
y-intercepts at 42; domain:
all real numbers, range: y <
– –2 or y >
–2
19. center (0, 0), x-intercepts at 43,
no y-intercepts; domain: x <
– –3 or x >
– 3,
range: all real numbers
23. 19
24. 17
25. 18
26. 20
27. 21
28. 22
20. center (0, 0), x-intercepts at 48,
y-intercepts at 44; domain: –8 <
–x<
– 8, 29.
range: –4 <
–y <
–4
21. center (0, 0), x-intercepts at 43,
y-intercepts at 45; domain: –3 <
–x<
– 3,
range: –5 <
–y <
–5
Hyperbola: center (0, 0), x-intercepts
22. center (0, 0), no x-intercepts,
y-intercepts at 43; domain:
±4, the lines of symmetry are the xall real numbers; range: y <
and y-axes; domain: x <
– –3 or y >
–3
– –4 or x >
– 4,
range: all real numbers.
10-1
7
Lesson 10-2
24. (0, 0), (6, 0), x = –6
26. (0, 0), (3, 0), x = –3
28. (0, 0), (0, 1), y = –1
25. (0, 0), (0, –1), y = 1
27. (0, 0), 25 , 0 , x = – 25
29. (0, 0), (0, –1), y = 1
4
4
8
Lesson 10-2
30. (2, 0), (2, 1), y = –1
32. (–2, 4), –2, 17 , y = 15
34. (4, 0), (4, –6), y = 6
31. (0, 0), (–2, 0), x = 2
33. (–3, 0), – 3 , 0 , x = – 9
35. (3, –1), (6, –1), x = 0
4
2
10-2
4
2
9
Lesson 10-2
36. x = 1 y2
43. x = – 1 y2
37. y
44. y = 1 x2
38. y
39. x
40. x
41. y
42.
12
1 2
=
x
400
= – 1 x2
20
= – 1 y2
28
= – 1 y2
36
= – 5 x2
56
8
48.
4
45. x = y2
46.
49.
47.
50.
10
Lesson 10-3
24. (–6, 0), 11
29.
32.
30.
33.
25. (–2, –4), 16
26. (3, 7), 4
6
27.
28.
31.
34.
10-3
11
Lesson 10-3
pages 552–554 Exercises
12. (x + 1)2 + (y – 3)2 = 81
1. x2 + y2 = 100
13. x2 + (y + 5)2 = 100
2. (x + 4)2 + (y + 6)2 = 49
14. (x – 3)2 + (y – 2)2 = 49
3. (x – 2)2 + (y – 3)2 = 20.25
15. (x + 6)2 + (y – 1)2 = 20
4. (x + 6)2 + (y – 10)2 = 1
16. (x – 5)2 + y2 = 50
5. (x – 1)2 + (y + 3)2 = 100
17. (x + 3)2 + (y – 4)2 = 9
6. (x + 5)2 + (y + 1)2 = 36
18. (x – 2)2 + (y + 6)2 = 16
7. (x + 3)2 + y2 = 64
19. (1, 1), 1
8. (x + 1.5)2 + (y + 3)2 = 4
20. (–2, 10), 2
9. x2 + (y + 1)2 = 9
21. (3, –1), 6
10. (x + 1)2 + y2 = 1
22. (–3, 5), 9
11. (x – 2)2 + (y + 4)2 = 25
23. (0, –3), 5
10-3
12
Lesson 10-3
58. (0, 4),
66. parabola; x = (y + 2)2 + 3;
11
59. (–5, 0), 3
2
60. (–2, –4), 5
61. (–3, 5),
2
38
62. (–1, 0), 2
67. Let P(x, y) be any point on the circle
centered at the origin and having radius r.
If P(x, y) is one of the points (r, 0), (–r, 0),
64. (0, 2), 2 5
(0, r), or (0, –r), substitution shows that
65. circle; (x – 4)2 + (y – 3)2 = 16;
x2 + y2 = r 2. If P(x, y) is any other point on
the circle, drop a perpendicular PK from P to
the x-axis (K on the x-axis). OPK is a right
triangle with legs of lengths |x| and |y| and
with hypotenuse of length r. By the
Pythagorean Theorem, |x|2 + |y|2 = r 2.
But |x|2 = x2 and |y|2 = y2. So x2 + y2 = r 2.
63. (3, 1),
6
10-3
13
Lesson 10-4
pages 559–561 Exercises
1.
x2
+
y2
=1
9
16
x2
2. 4 + y2 = 1
x2
3. 9 + y2 = 1
y2
2
4. x + 36 = 1
y2
x2
5.
+ 49 = 1
16
y2
x2
6.
+
=1
25
36
y2
x2
7.
+ 4 =1
81
2
y2
8. x +
=1
25
9
y2
x2
9.
+
=1
2.25 0.25
10.
11.
12.
13.
14.
15.
16.
17.
y2
x2
+
=1
256
64
x2 + y2 = 1
100
36
y2
x2
+ 25 = 1
12.25
y2
x2
+ 49 = 1
196
y2
2
x + 16 = 1
y2
x2
+
=1
256 12.25
y2
x2
+ 400 = 1
900
y2
2
x + 6.25 = 1
18. (0,
5), (0, –
5)
19. (0, 4), (0, –4)
14
Lesson 10-4
20. (4
2, 0), (–4
21. (8, 0), (–8, 0)
2, 0)
22. (0, 6), (0,–6)
23. (0,
6), (0, –
24. (2
6)
3, 0), (–2
3, 0)
25. (9, 0), (–9, 0)
15
Lesson 10-4
26. (3
15, 0), (–3
15, 0) 33. (
5, 0), (–
34. (0, 2
3), (0, –2
3)
35. (0, 4
2), (0, –4
2)
36. (0,
27.
28.
29.
30.
31.
32.
x2
100
x2
64
x2
89
x2
4
x2
245
x2
514
y2
+ 64 = 1
+
+
+
+
+
y2
=1
128
y2
=1
64
y2
20 = 1
y2
=1
49
y2
=1
225
41. a. 0.9;
5, 0)
37. (0, 2
21), (0, –
7), (0, –2
21)
7)
b. 0.1;
38. (0, 1), (0, –1)
39. (–3, 8), (–3, 2)
40. (–2,
2), (–2, –
2)
c. The shape is close
to a circle.
d. The shape is close
to a line segment.
10-4
16
Lesson 10-4
x2
y2
42.
+
=1
20.25
4
47.
43. a. Yes; since c2 = a2 – b2, if the
foci are close to 0, then c2 will
be close to 0 and a2 will be close
to b2. This means a will be close
to b and hence the ellipse will be
close to a circle.
b. If F1 and F2 are considered distinct
pts., then a circle is not an ellipse.
If F1 and F2 are the same pt., then
a circle is an ellipse.
y2
x2
44.
+ 4 =1
9
x2
45.
+ y2 = 1
16
y2
2
46. x + 9 = 1
y2
x2
+ 16 = 1
4
48. The vertices are the points farthest
from the center and the co-vertices
are the points closest to the center.
49. Check students’ work.
50.
51.
52.
53.
54.
55.
10-4
y2
x2
+ 3
4
y2
x2
+ 4
25
y2
x2
+ 81
121
x2
+
702.25
y2
x2
+
169 144
y2
x2
+
256 324
=1
=1
=1
y2
210.25 = 1
=1
=1
17
Lesson 10-5
pages 566–568 Exercises
1.
3.
5.
4.
6.
2.
10-5
18
Lesson 10-5
7.
9.
8.
10. (0,
11. (0,
97), (0, –
113)
97)
12. (
10-5
113), (0, –
265, 0), (–
265, 0)
19
Lesson 10-5
y2
x2
–
=1
96,480
69,169
y2
x2
20.
–
=1
240,000 10,000
2
y2
x
21.
–
=1
170,203,465
192,432,384
y2
x2
22.
–
=1
11
12
5.270 × 10
1.865 × 10
2
2
y
23. x –
=1
16
9
2
y2
24.
– x =1
25
144
2
25. y2 – x = 1
3
2
26. x – y2 = 1
4
19.
27.
30.
2
y2
– x =1
20.25
4
28.
2
31. y – x2 = 1
9
29.
10-5
20
Lesson 10-6
pages 573–576 Exercises
1.
2.
3.
4.
5.
6.
7.
8.
9.
(y – 1)2
(x + 2)2
+
4
9
2
(y – 3)2
(x – 5)
+
36
16
(y + 4)2
x2
+
25 = 1
36
(y + 6)2
(x – 3)2
+
49
9
(y + 3)2
(x + 3)2
–
9
16
2
(x – 4)2
(y + 3)
–
32
4
(y – 2)2
(x + 1)2
–
40
9
(x + 1)2
(y + 1)2
–
56
25
2
(y – 1)2
x
–
=1
25
16
=1
=1
y2
(x – 150)2
10.
– 21,204 = 1
1296
y2
(x – 175)2
11.
– 28,689 = 1
1936
12. y = (x – 4)2 + 3; parabola, vertex (4, 3)
=1
=1
=1
13. (x + 6)2 + y2 = 81; circle, center (–6, 0), radius 9
=1
=1
10-6
21
Lesson 10-6
14.
(y – 3)2
(x + 1)2
+
= 1; ellipse,
9
3
center (–1, 3), foci (–1, 3 ±
1)2
3)2
15. (x –
+ (y +
= 13; circle,
center (1, –3), radius 13
6 )
16. (y – 2)2 – (x – 3)2 = 1; hyperbola,
center (3, 2), foci (3, 2 ± 2)
17.
(x – 1)2
– (y + 1)2 = 1; hyperbola,
4
center (1, –1), foci (1 ±
10-6
5 , –1)
22
Lesson 10-6
18. x2 + (y + 7)2 = 36; circle,
center (0, –7), radius 6
19. x – 3 = 1 (y – 2)2; parabola,
2
vertex (3, 2)
20.
(y – 3)2
(x + 2)2
+
= 1; ellipse,
4
9
center (–2, 3), foci (–2 ±
5, 3)
21. (x + 3)2 – (y – 5)2 = 1; hyperbola,
center (–3, 5), foci (–3 ± 2, 5)
10-6
23
Lesson 10-6
y2
(x – 1)2
22.
+ 4 = 1; ellipse,
16
center (1, 0), foci (1 ± 2
3, 0)
y2
x2
24. Translate the equation
– 8 = 1,
16
a hyperbola centered at (0, 0), 3 units left.
25. a. hyperbola
b. line
26. a. h is added to each x-coordinate,
and k is added to each y-coordinate.
b. The lengths of the major and minor axes
are unchanged; the x-coordinates of the
2
2
x
(y + 3)
vertices are increased (or decreased) by
23. 4 –
= 1; hyperbola,
9
the same amount, and the same is true
center (0, –3), foci (± 13, –3)
for the y-coordinates. A similar remark
holds for the co-vertices.
10-6
24