Copyright

Ch 2: Analytical Geometry in Precalculus

About This Chapter

Watch the lesson videos in this chapter to review the topics of analytical geometry, including linear equations, standard parabolas, hyperbolas, and the standard equations for circles and ellipses.

Analytical Geometry in Precalculus - Chapter Summary

This chapter can help you refresh your knowledge of analytical geometry. Watch as our professional instructors explain linear equations on the x-y axis and standard equations for circles and ellipses. Then discover how to graph these geometric forms as the instructors walk you through example problems. If at any time you become confused on any of these topics, ask our instructors for clarification so that you can master the material on:

  • The equation for straight lines on the x-y axis
  • Characteristics of standard parabolas
  • Area and circumference of a circle
  • Formula for a circle
  • Finding a circle's center and radius on a graph
  • How to use the standard equation for ellipses
  • The characteristics of hyperbolas

Watch these brief videos then take quizzes that will help you reinforce the material discussed and point out areas you may still want to review. Print out the worksheets to review these concepts on your own. When reviewing areas of weakness, use video tags found on the timeline of each video to go to key parts of the lesson videos. Transcripts are available that present the same information covered in the videos but in an alternative written format.

6 Lessons in Chapter 2: Analytical Geometry in Precalculus
Test your knowledge with a 30-question chapter practice test
Identifying the Line of Symmetry: Definition & Examples

1. Identifying the Line of Symmetry: Definition & Examples

The line of symmetry, or the invisible line in the center of a shape or line, can be identified algebraically or graphically. Discover more about the line of symmetry, including how to find it using a graph, using a formula, and some examples of them.

The Parabola: Definition & Graphing

2. The Parabola: Definition & Graphing

In mathematics, a parabola is a u-shaped figure that looks similar to an arc. Learn about the definition, standard form equation, and how to graph a horizontal/vertical parabola.

Circles: Area and Circumference

3. Circles: Area and Circumference

Like all geometric shapes, circles take up space and a formula is required to calculate the area. Learn about the area and circumference of circles, explore the formula to calculate a circle's area, and review examples that use the diameter and others that use the circumference to find the area of a circle.

Graphing Circles: Identifying the Formula, Center and Radius

4. Graphing Circles: Identifying the Formula, Center and Radius

Graphing a circle requires knowing the center, radius, and circle formula. Changing the exponents in the formula changes the size and location on the graph. Learn how to to correctly graph a circle by identifying the formula, center, and radius.

Defining and Graphing Ellipses in Algebra

5. Defining and Graphing Ellipses in Algebra

An ellipse is a circle that has been stretched, with the horizontal path from the radius shorter than the vertical. Learn how to define the ellipse, and how the equation is used in the graphing of ellipses in algebra.

The Hyperbola: Definition, Vertices, Foci & Graphing

6. The Hyperbola: Definition, Vertices, Foci & Graphing

The standard equation of a hyperbola can be used to identify its vertices and foci for graphing. Learn the definition and standard equation of a hyperbola, understand how to identify its vertices and foci, and practice graphing with an example.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken
More Exams
There are even more practice exams available in Analytical Geometry in Precalculus.
Support