Name: ________________________ Class: ___________________ Date: __________
ID: A
Algebra 2B: Chapter 10 Test Practice
Multiple Choice
Identify the choice that best completes the statement or answers the question. .
____
1. Which is the equation of the parabola that has a vertex at the origin and a focus at (3, 0)?
1 2
1
x
a. y =
c. x = − y 2
12
12
1 2
1 2
y
b. y = − x
d. x =
12
12
2. Graph −3x 2 + 12y 2 = 84. Find the domain and range.
Write an equation of an ellipse in standard form with the center at the origin and with the given
characteristics.
3. height of 12 units and width of 19 units
Graph the equation. Describe the graph and its lines of symmetry.
4. 16x 2 + 9y 2 = 25
1
Name: ________________________
ID: A
5. x 2 + y 2 = 16
6. Write an equation for a graph that is the set of all points in the plane that are equidistant from the point F(6,
0) and the line x = –6.
7. Use the graph to write an equation for the parabola.
8. Write an equation of a parabola with a vertex at the origin and a focus at (0, –3).
2
Name: ________________________
ID: A
9. Find an equation that models the path of a satellite if its path is a hyperbola, a = 59,000 km, and c = 82,000
km. Assume that the center of the hyperbola is the origin and the transverse axis is horizontal.
10. This ellipse is being used for a design on a poster. Name the x-intercepts and y-intercepts of the graph.
3
Name: ________________________
ID: A
11. Write an equation in standard form for the circle.
Identify the conic section. If it is a parabola, give the vertex. If it is a circle, give the center and radius.
If it is an ellipse or a hyperbola, give the center and foci.
12. y 2 − 2x − 8y + 10 = 0
13. 5x 2 + 7y 2 + 30x − 42y + 73 = 0
14. Write an equation of an ellipse with center (5, –4), vertical major axis of length 8, and minor axis of length 6.
4
Name: ________________________
ID: A
15. Write an equation in standard form of an ellipse that has a vertex at (5, 0), a co-vertex at (0, –1), and is
centered at the origin.
16. Find the foci of the ellipse with the equation
17. Find the foci of the graph
y2
x2
+
= 1. Graph the ellipse.
4
36
y2
x2
−
= 1. Draw the graph.
36
25
18. Write an equation of a circle with center (2, 4) and radius 5.
19. Write an equation of a hyperbola with vertices (9, 4) and (–3, 4), and foci (13, 4) and (–7, 4).
2
2
20. Find the center and radius of the circle with equation (x − 8 ) + ÊÁË y − 5 ˆ˜¯ = 4.
5
ID: A
Algebra 2B: Chapter 10 Test Practice
Answer Section
MULTIPLE CHOICE
1. ANS: D
PTS: 1
DIF: L2
REF: 10-2 Parabolas
OBJ: 10-2.1 Writing the Equation of a Parabola
TOP: 10-2 Example 2
KEY: directrix | equation of a parabola | focus of a parabola | parabola
SHORT ANSWER
2. ANS:
The domain is all real numbers.The range is
ÏÔÔ
ÔÌÓ y | y ≤ − 7 and y ≥
PTS:
OBJ:
KEY:
3. ANS:
x2
90.25
¸Ô
7 ÔÔ˝ .
˛
1
DIF: L3
REF: 10-1 Exploring Conic Sections
10-1.1 Graphing Equations of Conic Sections
TOP: 10-1 Example 3
conic sections | domain | graphing | hyperbola | range
+
y2
= 1
36
PTS: 1
DIF: L2
REF: 10-4 Ellipses
OBJ: 10-4.1 Writing the Equation of an Ellipse
TOP: 10-4 Example 2
KEY: co-vertex of an ellipse | ellipse | equation of an ellipse | graphing | major axis of an ellipse | minor axis
of an ellipse | vertex of an ellipse
1
ID: A
4. ANS:
The graph is an ellipse. The center is at the origin. It has two lines of symmetry, the x-axis and the y-axis.
PTS: 1
DIF: L2
REF: 10-1 Exploring Conic Sections
OBJ: 10-1.1 Graphing Equations of Conic Sections
TOP: 10-1 Example 2
KEY: conic sections | graphing | ellipse | domain | range
5. ANS:
The graph is a circle of radius 4. Its center is at the origin. Every line through the center is a line of
symmetry.
PTS: 1
DIF: L2
REF: 10-1 Exploring Conic Sections
OBJ: 10-1.1 Graphing Equations of Conic Sections
TOP: 10-1 Example 1
KEY: conic sections | graphing | circle | domain | range
6. ANS:
1 2
x =
y
24
PTS: 1
DIF: L2
REF: 10-2 Parabolas
OBJ: 10-2.1 Writing the Equation of a Parabola
TOP: 10-2 Example 1
KEY: parabola | focus of a parabola | directrix | equation of a parabola
2
ID: A
7. ANS:
x2
y =
4
PTS: 1
DIF: L3
REF: 10-2 Parabolas
OBJ: 10-2.1 Writing the Equation of a Parabola
TOP: 10-2 Example 2
KEY: directrix | equation of a parabola | focus of a parabola | graphing | parabola | vertex of a parabola
8. ANS:
1
y = − x2
12
PTS: 1
DIF: L2
REF: 10-2 Parabolas
OBJ: 10-2.1 Writing the Equation of a Parabola
TOP: 10-2 Example 2
KEY: equation of a parabola | focus of a parabola | parabola | vertex of a parabola
9. ANS:
y2
x2
−
= 1
(3, 481, 000, 000) (3, 243, 000, 000)
PTS: 1
DIF: L2
REF: 10-5 Hyperbolas
OBJ: 10-5.2 Using the Foci of a Hyperbola
TOP: 10-5 Example 3
KEY: equation of a hyperbola | foci of a hyperbola | equation of a hyperbola | word problem
10. ANS:
(±1.5, 0), (0, ±3)
PTS: 1
DIF: L2
OBJ: 10-1.2 Identifying Conic Sections
KEY: conic sections | ellipse | intercepts
11. ANS:
2
2
(x + 1 ) + ÊÁË y + 3 ˆ˜¯ = 4
REF: 10-1 Exploring Conic Sections
TOP: 10-1 Example 4
PTS: 1
DIF: L2
REF: 10-3 Circles
OBJ: 10-3.1 Writing the Equation of a Circle
TOP: 10-3 Example 3
KEY: circle | equation of a circle | graphing | center of a circle | radius
12. ANS:
parabola; vertex (–3, 4)
PTS: 1
DIF: L2
REF: 10-6 Translating Conic Sections
OBJ: 10-6.2 Identifying Translated Conic Sections
TOP: 10-6 Example 4
KEY: conic sections | equation of a parabola | completing the square | translation | vertex of a parabola
13. ANS:
ellipse with center (–3, 3), foci at (−3 ± 2, 3)
PTS: 1
DIF: L2
REF: 10-6 Translating Conic Sections
OBJ: 10-6.2 Identifying Translated Conic Sections
TOP: 10-6 Example 4
KEY: conic sections | co-vertex of an ellipse | equation of an ellipse | foci of an ellipse | major axis of an
ellipse | minor axis of an ellipse | translation | vertex of an ellipse | completing the square
3
ID: A
14. ANS:
(x − 5)
9
2
ÊÁ y + 4 ˆ˜ 2
Ë
¯
+
= 1
16
PTS: 1
DIF: L2
REF: 10-6 Translating Conic Sections
OBJ: 10-6.1 Writing Equations of Translated Conic Sections
TOP: 10-6 Example 1
KEY: conic sections | co-vertex of an ellipse | equation of an ellipse | major axis of an ellipse | minor axis of
an ellipse | translation | vertex of an ellipse
15. ANS:
y2
x2
+
= 1
25
1
PTS: 1
DIF: L2
REF: 10-4 Ellipses
OBJ: 10-4.1 Writing the Equation of an Ellipse
TOP: 10-4 Example 1
KEY: ellipse | equation of an ellipse | vertex of an ellipse | co-vertex of an ellipse | minor axis of an ellipse |
major axis of an ellipse
16. ANS:
foci (0, ± 4 2 )
PTS: 1
DIF: L2
REF: 10-4 Ellipses
OBJ: 10-4.2 Finding and Using the Foci of an Ellipse
TOP: 10-4 Example 3
KEY: co-vertex of an ellipse | ellipse | equation of an ellipse | graphing | foci of an ellipse | major axis of an
ellipse | minor axis of an ellipse
4
ID: A
17. ANS:
( ± 61 , 0)
PTS: 1
DIF: L2
REF: 10-5 Hyperbolas
OBJ: 10-5.2 Using the Foci of a Hyperbola
TOP: 10-5 Example 2
KEY: asymptotes of a hyperbola | equation of a hyperbola | graphing | hyperbola | transverse axis of a
hyperbola | vertices of a hyperbola | foci of a hyperbola
18. ANS:
2
2
(x − 2 ) + ÁÊË y − 4 ˜ˆ¯ = 25
PTS: 1
DIF: L2
REF: 10-3 Circles
OBJ: 10-3.1 Writing the Equation of a Circle
KEY: center of a circle | circle | equation of a circle | radius
19. ANS:
ÊÁ y − 4 ˆ˜ 2
(x − 3) 2
Ë
¯
−
= 1
36
64
TOP: 10-3 Example 1
PTS: 1
DIF: L2
REF: 10-6 Translating Conic Sections
OBJ: 10-6.1 Writing Equations of Translated Conic Sections
TOP: 10-6 Example 2
KEY: conic sections | equation of a hyperbola | hyperbola | translation | transverse axis of a hyperbola |
vertices of a hyperbola
20. ANS:
(8, 5); 2
PTS: 1
DIF: L2
REF: 10-3 Circles
OBJ: 10-3.2 Using the Center and Radius of a Circle
TOP: 10-3 Example 4
KEY: center of a circle | circle | equation of a circle | radius | translation
5