Chapter 10 – Conic Sections 10.1
Answer Key
Parabolas with Vertex at the Origin
Answers 1.
up
2.
left
3.
down
4.focus: (0, 0.5), directrix: y = 0.5 5.focus: (0.0625, 0), directrix: x = 0.0625 6.focus: (1.25, 0), directrix: x = 1.25 7.focus: (0, 2), directrix: y = 2
ans100101
CK12 Algebra II with Trigonometry Concepts
1
Chapter 10 – Conic Sections 8.focus: (0.125, 0), directrix: x = 0.125
Answer Key ans100102
9.focus: (0, 0.75), directrix: y = 0.75
ans100103
10.
11. 12.
13.
, p and a have an inverse relationship.
14.see worked out s olution key
CK12 Algebra II with Trigonometry Concepts
2
Chapter 10 – Conic Sections
Answer Key
15.16 inches above the vertex
CK12 Algebra II with Trigonometry Concepts
3
Chapter 10 – Conic Sections 10.2
Answer Key
Parabolas with Vertex at (h , k )
Answers 1.vertex: (1, 6), focus: (1, 5.25), directrix: y = 6.75, axis: x = 1 2.vertex: (3, 7), focus: (3, 7.25), directrix: y = 6.75, axis: x = 3 3.vertex: (1, 2), focus: (1, 2), directrix: x = 3, axis: y = 2 4.vertex: (3, 0), focus: (0.5, 0), directrix: x = 5.5, axis: y = 0 5.vertex: (6, 8), focus: (6, 7), directrix: y = 9, axis: x = 6 6.vertex: (0, 5), focus: (0.125, 5), directrix: x = 0.125, axis: y = 5 7.ans100104
8.ans100105
CK12 Algebra II with Trigonometry Concepts
4
Chapter 10 – Conic Sections
Answer Key
9.ans100106
10.ans100107
11.
12.
13. 14. 15.
, vertex is (4, 3)
CK12 Algebra II with Trigonometry Concepts
5
Chapter 10 – Conic Sections
Answer Key
CK12 Algebra II with Trigonometry Concepts
6
Chapter 10 – Conic Sections 10.3
Answer Key
Circles with Center at the Origin
Answers 1.ans100201
2.ans100202
3.ans100203
CK12 Algebra II with Trigonometry Concepts
7
Chapter 10 – Conic Sections
Answer Key
4.ans100204
5.ans100205
6.ans100206
CK12 Algebra II with Trigonometry Concepts
8
Chapter 10 – Conic Sections
Answer Key
7.
8.
9.
10.
11.
12.
13.
no
14.
yes
15.
no
16.
a) b)
3
c)
17.
CK12 Algebra II with Trigonometry Concepts
9
Chapter 10 – Conic Sections 10.4
Answer Key
Circles with Center at (h , k )
Answers 1.
D
2.
B
3.
A
4.
C
5.ans100207
6.ans100208
CK12 Algebra II with Trigonometry Concepts
10
Chapter 10 – Conic Sections
Answer Key
7.ans100209
8.
9.
10.
11.
12.
13.
14.No, because
15.
16.
.
CK12 Algebra II with Trigonometry Concepts
11
Chapter 10 – Conic Sections 10.5
Answer Key
Ellipses with Center at the Origin
Answers 1.vertices: (0, ±4 ), covertices: (±3, 0),
foci:
2.
vertices: (±5, 0), covertices: (0, ±2),
ans100301
foci:
ans100302
3.vertices: ( ±8 , 0), covertices: (0, ±1),
foci:
ans100303
4.
vertices: (±10, 0), covertices: (0, ±9),
foci:
ans100304
CK12 Algebra II with Trigonometry Concepts
12
Chapter 10 – Conic Sections 5.vertices: ( ±7 , 0), covertices: (0, ±2),
foci:
ans100305
Answer Key 6.
vertices: (0, ±11), covertices: (±3, 0),
foci:
ans100306
7.
8.
9.
10.
11.
12.
13.
CK12 Algebra II with Trigonometry Concepts
13
Chapter 10 – Conic Sections 10.6
Answer Key
Ellipses with Center at (h , k )
Answers 1.
center: (5, 1), vertices: (5, 7) and (5, 5), covertices: (0, 1) and (10, 1), foci:
2.
center: (2, 6), vertices: (6, 6) and (4, 6), covertices: (2, 5) and (2, 7), foci:
3.
center: (5, 1), vertices: (5, 7) and (5, 5), covertices: (0, 1) and (10, 1), foci:
4.
center: (0, 6), vertices: (8, 6) and (8, 6), covertices: (0, 1) and (0, 11), foci:
5.
center: (8, 4), vertices: (8, 1) and (8, 7), covertices: (7, 4) and (9, 4), foci:
6.
center: (4, 5), vertices: (4, 4) and (4, 13), covertices: (2, 5) and (6, 5), foci:
7.ans100107
8.
ans100108
CK12 Algebra II with Trigonometry Concepts
14
Chapter 10 – Conic Sections
Answer Key
CK12 Algebra II with Trigonometry Concepts
15
Chapter 10 – Conic Sections 9.ans100109
Answer Key 10.
ans100110
11.
12.
13.
14.
15.
CK12 Algebra II with Trigonometry Concepts
16
Chapter 10 – Conic Sections 10.7
Answer Key
Graphing Hyperbolas Centered at the Origin
Answers
1.( ±3 , 0), (± 5 , 0),
2.(0, ±5 ),
,
3.( ±9 , 0),
,
4.( ±4 , 0),
,
5.(0, ±7 ),
,
6.(0, ±3 ),
7.(0, ±1 ),
,
,
8.( ±8 , 0),
,
9.(0, ±4 ),
,
10.ans100401
CK12 Algebra II with Trigonometry Concepts
17
Chapter 10 – Conic Sections
Answer Key
11.ans100402
12.ans100403
CK12 Algebra II with Trigonometry Concepts
18
Chapter 10 – Conic Sections
Answer Key
13.ans100404
14.Answers will vary.
15.Foci are
and
.
CK12 Algebra II with Trigonometry Concepts
19
Chapter 10 – Conic Sections 10.8
Answer Key
Writing the Equation of a Hyperbola, Centered at the Origin
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
or
11.
or
CK12 Algebra II with Trigonometry Concepts
20
Chapter 10 – Conic Sections
12.
or
13.
or
14.
15.
Answer Key
CK12 Algebra II with Trigonometry Concepts
21
Chapter 10 – Conic Sections 10.9
Answer Key
Hyperbolas Centered at (h , k )
Answers
1.(5.1), (0, 1) and (10, 1),
,
2.(6, 2), (6, 2) and (6, 6),
3.(3, 2), (3, 5) and (3, 1),
4.(0, 6), (8, 6) and (8, 6),
5.(8, 4), (7, 4) and (9, 4),
,
,
,
,
6.(5, 4), (5, 2) and (5, 6), 7.ans100405
, 8.
ans100406
CK12 Algebra II with Trigonometry Concepts
22
Chapter 10 – Conic Sections 9.ans100407
Answer Key 10.
ans100408
11.
12.
13.
14.
CK12 Algebra II with Trigonometry Concepts
23
Chapter 10 – Conic Sections
15.
Answer Key
CK12 Algebra II with Trigonometry Concepts
24
Chapter 10 – Conic Sections
Answer Key
10.10 General Conic Equation Answers 1.Answers will vary.
2.
3.
4.
5.
6.
7.
8.
9.
10.circle, (1, 1.5) 11.parabola, (1, 9) 12.ellipse, (2, 0.5) 13.hyperbola, (1.5, 1) 14.parabola, (5, 3) 15.hyperbola, (2, 7)
CK12 Algebra II with Trigonometry Concepts
25
Chapter 10 – Conic Sections
Answer Key
10.11 Classifying Conic Sections Answers 1.
circle
2. hyperbola 3.
ellipse
4. parabola 5. parabola 6.
circle
7.
C
8.
D
9.
A
10.
B
11.parabola 12. circle 13.hyperbola 14.parabola
CK12 Algebra II with Trigonometry Concepts
26
Chapter 10 – Conic Sections 15. a)
Answer Key
ans100501
b)
Yes
c)
d)
, the ellipses are s maller than the circle
CK12 Algebra II with Trigonometry Concepts
27
Chapter 10 – Conic Sections
Answer Key
10.12 Solving Systems of Lines, Quadratics, and Conics Answers 1.
(1, 8), (1, 3), (3, 2.5)
2.
(3, 7), 1, 2.75)
3.
(4, 0), (0, 3.5)
4.
(6.5, 6.5), (6. 3)
5.
(1.722, 0.722), (2.322, 3.322)
6.
(1.69, 2.155), (0.71, 2.645)
7.
( ±1 .076, 2.843), ( ±1 .610, 1.407)
8.
(0, 10), (2, 9)
9.
no s olution
10.
(1, 2), (2.67, 4.75)
11.
0, 1, 2, 3, or 4
12.
0, 1, 2, 3, or 4
13.
One possibility:
, the circle are concentric or do not
intersect.
14. 15.
(2, 2) and (2, 2)
CK12 Algebra II with Trigonometry Concepts
28
