Ch 27: NYSTCE Mathematics: Conic Sections

About This Chapter

Use this chapter to brush up on your knowledge of conic sections as you study for the NYSTCE Mathematics assessment. Watch fun video lessons to revisit the subject, then take self-assessment quizzes to reinforce lesson concepts.

NYSTCE Mathematics: Conic Sections - Chapter Summary

If you haven't explored the parabola, ellipses and hyperbolas in weeks, months or years, this is your chance to get reacquainted with these concepts, which will be examined on the NYSTCE Math assessment. Take time to explore short lessons in this chapter that ensure you're ready for the following on exam day:

  • Understanding the focus and directrix of a parabola
  • Explaining how to find the equation of a parabola from the focus and directrix
  • Describing foci, and sharing the definitions of ellipses and hyberbolas
  • Deriving the equation of an ellipse and hyperbola from the foci
  • Demonstrating your ability to solve conic sections problems

The lessons in this chapter are available in both video and written formats. Expert instructors provide you with comprehensive overviews of various conic sections concepts to ensure you're able to tackle this subject on the assessment. Watch the lessons in any sequence that works best for your studies, and revisit them as often as you'd prefer. At any point during your preparations, take self-assessment quizzes and a chapter exam to test your comprehension of the lessons, and gauge your readiness to take the assessment.

6 Lessons in Chapter 27: NYSTCE 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

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Other Chapters

Other chapters within the NYSTCE Mathematics (004): Practice & Study Guide course

Support