Dugopolski’s 87College Algebra
Chapter 7 Test — Form A Name: _________________________
Sketch the graph of each equation.
1. 2.
3. 4.
Determine the equation of each conic section.
5. A circle with center and radius .
5. _________________________
6. A parabola with focus and directrix .
6. _________________________
7. An ellipse with foci and -intercepts .
7. _________________________
88 Form 7A
8. A hyperbola with foci and vertices .
8. _________________________
Solve each problem.
9. Find the center and radius of the circle + .
9. _________________________
10. Find the vertex, focus, and the equation of the directrix for the parabola .
10. __________________vertex:
___________________focus:
________________directrix:
11. Find the equations of the asymptotes for the hyperbola .
11. _________________________
12. Find the foci, length of the major axis, and length of the minor axis for the
ellipse .
12. _____________________foci:
_______length of major axis:
_______length of minor axis:
Dugopolski’s 89College Algebra
Chapter 7 Test — Form B Name: _________________________
Sketch the graph of each equation.
1. 2.
3. 4.
Determine the equation of each conic section.
5. A circle with center and radius .
5. _________________________
6. A parabola with focus and directrix .
6. _________________________
7. An ellipse with foci and -intercepts .
7. _________________________
90 Form 7B
8. A hyperbola with foci and vertices .
8. _________________________
Solve each problem.
9. Find the center and radius of the circle + .
9. _________________________
10. Find the vertex, focus, and the equation of the directrix for the parabola
.
10. __________________vertex:
___________________focus:
________________directrix:
11. Find the equations of the asymptotes for the hyperbola .
11. _________________________
12. Find the foci, length of the major axis, and length of the minor axis for the ellipse
.
12. ____________________foci:
_______length of major axis:
_______length of minor axis:
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Inc.
Dugopolski’s 91College Algebra
Chapter 7 Test — Form C Name: _________________________
Sketch the graph of each equation.
1. 2.
3. 4.
Determine the equation of each conic section.
5. A circle with center and an -intercept of 6.
5. _________________________
6. A parabola with focus and vertex .
6. _________________________
7. An ellipse with foci and -intercepts .
7. _________________________
92 Form 7C
8. A hyperbola whose transverse axis has endpoints and whose conjugate axis
has endpoints .
8. _________________________
Solve each problem.
9. Find the center and radius of the circle .
9. _________________________
10. Find the vertex, focus, and the equation of the directrix for the parabola .
10. __________________vertex:
___________________focus:
_________________directrix:
11. Find the equations of the asymptotes for the hyperbola .
11. _________________________
12. Find the foci of the ellipse .
12. _________________________
Dugopolski’s 93College Algebra
Chapter 7 Test — Form D Name: _________________________
Sketch the graph of each equation.
1. 2.
3. 4.
Determine the equation of each conic section.
5. A circle with a diameter which has endpoints of and .
5. _________________________
6. A parabola with vertex and directrix .
6. _________________________
7. An ellipse with foci and -intercepts .
7. _________________________
94 Form 7D
8. A hyperbola with vertices of the fundamental rectangle at and and
with branches opening upwards and downwards.
8. _________________________
Solve each problem.
9. Find the center and radius of the circle .
9. _________________________
10. Find the vertex, focus, and the equation of the directrix for the parabola .
10. __________________vertex:
___________________focus:
________________directrix:
11. Find the equations of the asymptotes for the hyperbola .
11. _________________________
12. Find the foci of the ellipse
12. _________________________
Dugopolski’s 95College Algebra
Chapter 7 Test — Form E Name: _________________________
Multiple Choice: Choose the best answer for each problem.
_____ 1. Give the equation of the directrix for the parabola ( ) .
a. = 1 b. = 3 c. = 5 d. =
_____ 2. Give the equation of the parabola with vertex (2, 1) and directrix .
a. ( ) c. ( )
b. ( ) d. ( )
_____ 3. Which way does the graph of the parabola open ?
a. To the right b. To the left c. Up d. Down
_____ 4. Give an equation of the parabola with vertex and focus .
a. ( ) c. ( )
b. ( ) d. ( )
_____ 5. Write in the form ( ) .
a. ( ) c. ( )
b. ( ) d. ( )
_____ 6. Find the center of the circle whose equation is .
2
a. , b. ( , ) c. , d. ( , )
_____ 7. Give the equation of the ellipse with intercepts and .
a. b. c. d.
_____ 8. Write the equation of the circle with center and which passes through
the point .
a. ( ) ( ) c. ( ) ( )
b. ( ) ( ) d. ( ) ( )
_____ 9. Find the -intercepts for the ellipse .
a. ( , ), ( , ) c. ( , ), ( , )
b. ( , ), ( , ) d. ( , ), ( , )
96 Form 7E
_____ 10. Find the length of the major axis of the ellipse .
a. b. c. 2 d. 2
_____ 11. A compass is opened to a width of 2 units. The sharp end of the compass is
placed on a coordinate system 3 units to the left and 1 unit up from a point of
origin. Give the equation of the path traced by the pencil end of the compass.
a. ( ) ( ) c.
b. ( ) ( ) d. ( ) ( )
_____ 12. Give the equation of the hyperbola with intercepts , ,
and foci and .
a. b. c. d.
_____ 13. Give the equations of the asymptotes of the hyperbola .
a. = , = c. = , =
b. = , = d. = , =
_____ 14. What is the focus for the parabola ?
a. b. c. d.
9
8
_____ 15. Describe the graph of .
a. A hyperbola with branches opening up and down.
b. A hyperbola with branches opening right and left.
c. A circle with center (3, 1).
d. An ellipse with center (3, 1).
_____ 16. Define a hyperbola.
a. The set of points in a plane such that the difference between the distances
from two fixed points is a constant.
b. The set of points in a plane such that the sum of the distances from two
fixed points is a constant.
c. The set of points in a plane equidistant from a fixed point.
d. The set of points in a plane equidistant from a fixed line and a fixed point
not on the line.
Dugopolski’s 97College Algebra
Chapter 7 Test — Form F Name: _________________________
Multiple Choice: Choose the best answer for each problem.
_____ 1. Give the equation of the directrix for the parabola ( ) .
a. = 1 b. = 3 c. = 5 d. =
_____ 2. Give the equation of the parabola with vertex ( , ) and directrix .
a. ( ) c. ( )
b. ( ) d. ( )
_____ 3. Which way does the graph of the parabola open ?
a. To the right b. To the left c. Up d. Down
_____ 4. Give an equation of the parabola with vertex and focus .
a. ( ) c. ( )
b. ( ) d. ( )
_____ 5. Write in the form ( ) .
a. ( ) c. ( )
b. ( ) d. ( )
_____ 6. Find the center of the circle whose equation is .
2
a. , b. ( , ) c. , d. ( , )
_____ 7. Give the equation of the ellipse with intercepts and .
a. b. c. d.
_____ 8. Write the equation of the circle with center and which passes through
the point .
a. ( ) ( ) c. ( ) ( )
b. ( ) ( ) d. ( ) ( )
_____ 9. Find the -intercepts for the ellipse .
a. , , , c. , , ,
b. , d. , , ,
98 Form 7F
_____ 10. Find the length of the minor axis of the ellipse .
a. b. c. 2 d. 2
_____ 11. A compass is opened to a width of 2 units. The sharp end of the compass is
placed on a coordinate system 3 units to the right and 1 unit down from a point
of origin. Give the equation of the path traced by the pencil end of the
compass.
a. c.
b. d.
_____ 12. Give the equation of the ellipse with -intercepts and foci .
a. b. c. d.
20 6
_____ 13. Give the equations of the asymptotes of the hyperbola .
9 16
a. = , = c. = , =
b. = , = d. = , =
_____ 14. What is the focus of the parabola .
a. b. c. d.
_____ 15. Describe the graph of .
a. A hyperbola with branches opening up and down.
b. A hyperbola with branches opening right and left.
c. A circle with center (3, 1).
d. An ellipse with center (3, 1).
_____ 16. Define an ellipse.
a. The set of points in a plane such that the difference between the distances
from two fixed points is a constant.
b. The set of points in a plane such that the sum of the distances from two
fixed points is a constant.
c. The set of points in a plane equidistant from a fixed point.
d. The set of points in a plane equidistant from a fixed line and a fixed point
not on the line.
Dugopolski’s 125College Algebra
Chapter Test Keys
CHAPTER 7
126 Chapter 7 Test Key