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Ch 40: PLACE Mathematics: Conic Sections

About This Chapter

This chapter explores arcs, focus points, curves and other parts of conic sections to help you prepare for Colorado's math educator licensing exam. Video lessons and quizzes are both available to give you ample information and practice before taking the PLACE Mathematics test.

PLACE Mathematics: Conic Sections - Chapter Summary

The lessons in this chapter can help you remember how to use equations to describe shapes and ways to measure distances. The easy-to-follow video lessons explain other topics you'll encounter on the exam including:

  • Identifying the focus and directrix of a parabola
  • Writing the equation of a parabola
  • Foci, ellipses and hyperbolas
  • Using the foci to find the equation of an ellipse and a hyperbola

There are multiple-choice quizzes at the end of every lesson so you can see how well you retained the information and have an opportunity to answer exam-type questions.

Objectives of the PLACE Mathematics: Conic Sections Chapter

The PLACE Mathematics exam tests your ability to apply formulas involving circles and arcs to solve equations. The topics in the Conic Sections chapter are part of the Measurement and Geometry portion of the exam. This portion constitutes about 19% of the PLACE Mathematics test as a whole, which means that 19 of the 100 questions on the test will cover measurement and geometry. All questions are multiple-choice and require you to pick the correct answer.

6 Lessons in Chapter 40: PLACE Mathematics: Conic Sections
Test your knowledge with a 30-question chapter practice test
The Focus and Directrix of a Parabola

1. 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.

Finding the Equation of a Parabola from the Focus and Directrix

2. 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

3. 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.

Derive the Equation of an Ellipse from the Foci

4. 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.

Derive the Equation of a Hyperbola from the Foci

5. 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.

Practice with the Conic Sections

6. 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.

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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Other Chapters

Other chapters within the PLACE Mathematics: Practice & Study Guide course

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