Unit TenAlgebra II Practice TestConic Sections

Name______Period_____Date______

NON-CALCULATOR SECTION

Vocabulary: Define each word and give an example.

  1. Major Axis (of an ellipse)
  1. Hyperbola
  1. Directrix

Short Answer:

  1. Describe how to determine the discriminant from the equation . If the discriminant is less than 0, what type of conic section does the equation represent?
  1. Write the standard form of an equation of a hyperbola centered at the point .

Review:

  1. Perform the indicated operation:
  1. Find an equation for the inverse of the function:
  1. Find the inverse of the matrix .

Problems:

**Be sure to show all work used to obtain your answer. Circle or box in the final answer.**

  1. Graph the equation:

a. b.

c. d.

e. f.

  1. 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. circleB. ellipseC. parabolaD. hyperbola

  1. What conic does the equation represent? ______
  2. What conic does the equation represent? ______
  3. What conic does the equation represent? ______
  4. What conic does the equation represent? ______
  5. What conic does the equation represent? ______

Multiple Choice Section: Circle the correct answer.

  1. What is the equation of the graph?
  1. Which graph best represents the graph of ?

A.B.C.D.

  1. Which is the equation of a parabola?

Name: ______Period______Date______

CALCULATOR SECTION

Directions: Show all work. A calculator may not be necessary to solve some of the problems.

  1. Write an equation for the conic section:
  2. Parabola with vertex at and focus at .
  1. Circle with center at and radius .
  1. Ellipse with vertices at and , and co-vertices at and .
  1. Ellipse with center at , vertices at and , and co-vertices at and .
  1. Hyperbola with vertices at and and foci at and .
  1. Hyperbola with foci at and and asymptote with slope .
  1. Classify the conic section and write its equation in standard form:

a. b.

c. d.

e. f.

  1. The cross section of a television antenna dish is a parabola. The receiver is located at the focus, 5 feet above the vertex. Find an equation for the cross section of the dish. (Assume the vertex is at the origin.) If the television antenna dish is 10 feet wide, how deep is it?

Equation: ______

Depth: ______

Page 1 of 6McDougal Littell: 10.1 – 10.6