Algebra II Test
Unit Ten – Conic Sections
Good Luck ToJ______Period_____Date______
NON-CALCULATOR SECTION
Vocabulary: Define each word and give an example.
1. Minor Axis (of an ellipse)
2. Circle
3. Focus (of a parabola)
Short Answer:
4. Describe how to determine the discriminant from the equation . If the discriminant is greater than 0, what type of conic section does the equation represent?
5. Write the standard form of the equation of an ellipse centered at the point .
Review:
6. Perform the indicated operation:
7. Find an equation for the inverse of the function:
8. Find the determinant of the matrix
Problems:
**Be sure to show all work used to obtain your answer. Circle or box in the final answer.**
9. Graph the equation:
a. b.
c. d.
e. f.
10. Find the distance between the two points. Then find the midpoint of the line segment connecting the two points.
a. distance: ______b. distance: ______
midpoint: ______midpoint: ______
Use the choices below to answer the following:
A. circle B. ellipse C. parabola D. hyperbola
11. What conic does the equation represent? ______
12. What conic does the equation represent? ______
13. What conic does the equation represent? ______
14. What conic does the equation represent? ______
15. What conic does the equation represent? ______
Multiple Choice Section: Circle the correct answer.
16. Which graph best represents the equation ?
A. B. C. D.
17. What is the equation for the graph?
A.
B.
C.
D.
18. What equation represents the graph?
A.
B.
C.
D.
Algebra II Test
Unit Ten – Conic Sections
Good Luck ToJ______Period_____Date______
CALCULATOR SECTION
Directions: Show all work. A calculator may not be necessary to solve some of the problems.
19. Write an equation for the conic section:
a. Parabola with vertex at and directrix .
b. Circle with center at and passing through .
c. Circle with center at and radius .
d. Ellipse with center at , x-intercepts and , and y-intercepts and .
e. Ellipse with center at , vertex and co-vertex .
f. Hyperbola with center , foci at and , and vertices at and .
g. Hyperbola with foci at and and vertices at and .
20. Classify the conic section and write its equation in standard form:
a. b.
c. d.
e. f.
21. A searchlight reflector is designed so that a cross section through its axis is a parabola and the light source is at the focus. Find the focus if the reflector is 3 feet across at the opening and 1 foot deep.
Page 6 of 6 McDougal Littell: 10.1 – 10.6 Algebra II Unit 10 Test