Ch 9: Parabolas, Ellipses and Hyperbolas

About This Chapter

Simplify the learning process with these lessons on parabolas, ellipses and hyperbolas, which includes equations derived from the foci and plenty of examples. The short lessons and quizzes in this chapter are a quick way to get ready for an upcoming exam.

Parabolas, Ellipses and Hyperbolas - Chapter Summary

By studying these lessons, you'll boost your knowledge of parabolas, ellipses and hyperbolas. For instance, you can review how to use the foci to derive the equation of a hyperbola. This chapter can also help you better understand parabolas in intercept, standard, and vertex form. After completing the lessons, you should be ready to do the following:

  • Provide a definition for parabola
  • Discuss different forms of parabolas
  • Outline the focus and directrix of a parabola
  • Give an example of an ellipse
  • Use the foci to derive the equation of an ellipse
  • Provide an example of a hyperbola

The short video lessons in this chapter can help you gain a better understanding of parabolas, ellipses and hyperbolas. If you get stuck on a topic, you can submit questions to our experts. You can also take a self-assesment quiz that's available for each lesson to test your knowledge of the topics in the chapter. You can track the progress that you make from your personal Dashboard.

7 Lessons in Chapter 9: Parabolas, Ellipses and Hyperbolas
Test your knowledge with a 30-question chapter practice test
What is a Parabola?

1. What is a Parabola?

A parabola is the U shape that we get when we graph a quadratic equation. We actually see parabolas all over the place in real life. In this lesson, learn where, and the correct vocab to use when talking about them.

Parabolas in Standard, Intercept, and Vertex Form

2. Parabolas in Standard, Intercept, and Vertex Form

By rearranging a quadratic equation, you can end up with an infinite number of ways to express the same thing. Learn about the three main forms of a quadratic and the pros and cons of each.

The Focus and Directrix of a Parabola

3. The Focus and Directrix of a Parabola

In this lesson, we will review what a parabola is, then we will look at the formal definition of a parabola, introducing the focus and directrix of a parabola. We will look at some examples to help solidify our understanding of these concepts.

Ellipse: Definition, Equation & Examples

4. Ellipse: Definition, Equation & Examples

This lesson will cover the definition of ellipses and the standard form equation of an ellipse. It will also examine how to determine the orientation of an ellipse and how to graph them.

Derive the Equation of an Ellipse from the Foci

5. Derive the Equation of an Ellipse from the Foci

In this lesson, you're going to learn the definition of an ellipse and foci, the standard forms of the equation for an ellipse, and how to find such an equation when given the foci.

Hyperbola: Definition, Formula & Examples

6. Hyperbola: Definition, Formula & Examples

Hyperbolas are a set of two similar curves called branches set on a plane governed by certain equations. They are, along with circles, parabolas and ellipses, conic sections, as you'll learn in this lesson.

Derive the Equation of a Hyperbola from the Foci

7. Derive the Equation of a Hyperbola from the Foci

This lesson will go over what a hyperbola is and walk through the steps of finding the equation of a hyperbola given just the foci and vertex. After learning the process, we will look at an example of finding a hyperbola equation given this information.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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