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