About This Chapter
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.
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.
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.
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.
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.
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.
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.
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.
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Other chapters within the CLEP Precalculus: Study Guide & Test Prep course
- Recognizing Functions
- Working with Exponential and Logarithmic Functions
- Piecewise and Composite Functions
- Functions as Models
- Understanding, Solving & Graphing Inequalities
- Understanding Linear Equations
- Radical, Rational and Absolute Value Equations
- Factoring & Solving Quadratic Equations
- Exponents and Polynomials
- Geometry and Trigonometry
- Using Scientific Calculators
- CLEP Precalculus Flashcards
- Additional CLEP Precalculus Flashcards