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Ch 10: High School Geometry: Conic Sections

About This Chapter

Watch online math video lessons and learn about hyperbolas, parabolas, ellipses and more. Take the quizzes that follow each lesson to test your knowledge of conic sections.

High School Geometry: Conic Sections - Chapter Summary and Learning Objectives

Get an introduction to the shapes you get when a plane and a cone intersect. Instructors teaching this chapter's video lessons illustrate the components of hyperbolas, ellipses and parabolas with plenty of examples. There are even multiple-choice quizzes and practice problems you can use to affirm your understanding of these conic sections and the steps involved in writing their equations. By the end of this chapter, you should be able to do the following:

  • Differentiate between a parabola, hyperbola and ellipse
  • Identify a conic section's focus or foci
  • Derive a conic section's equation using its focus or foci

Video Objectives
The Focus and Directrix of a Parabola Identify a parabola's focus and directrix when presented with its graph.
Finding the Equation of a Parabola from the Focus and Directrix Find out how a parabola's directrix and focus can be used to write its equation.
Foci and the Definitions of Ellipses and Hyperbolas Describe the relationship between each of these conic section's directrix and the distance from its foci.
Derive the Equation of an Ellipse from the Foci Explore methods for writing an ellipse's equation when given its foci.
Derive the Equation of a Hyperbola from the Foci Learn how to write equations for hyperbolas when given their foci.
Practice with the Conic Sections Practice writing equations for parabolas, hyperbolas and ellipses.

6 Lessons in Chapter 10: High School Geometry: Conic Sections
Test your knowledge with a 30-question chapter practice test
Derive the Equation of a Hyperbola from the Foci

1. 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.

Derive the Equation of an Ellipse from the Foci

2. 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.

Finding the Equation of a Parabola from the Focus and Directrix

3. Finding the Equation of a Parabola from the Focus and Directrix

A parabola is the familiar shape seen in many physical applications, like the path taken by a ball thrown upwards. This lesson explores equations for the parabola and shows how they may be obtained from two quantities: the focus and the directrix.

Foci and the Definitions of Ellipses and Hyperbolas

4. Foci and the Definitions of Ellipses and Hyperbolas

In this lesson, we'll look at the definition of an ellipse and a hyperbola. We'll use the foci of each of these to define them technically and formally, and we'll look at some examples to make the definitions more understandable.

Practice with the Conic Sections

5. Practice with the Conic Sections

Conic sections are shapes created by cutting through a 3D cone. In this lesson, learn how to identify each conic section from its graph and characteristic equation.

The Focus and Directrix of a Parabola

6. 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.

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

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