About This Chapter
Conic Sections - Chapter Summary and Learning Objectives
Anyone who has ever eaten an ice cream cone or donned a party hat is familiar with this geometric shape, but have you ever studied the curves you get when a cone is intersected by a plane? Let our experienced instructors improve your geometry knowledge with lessons on conic sections, such as ellipses, hyperbolas and parabolas. The illustrated videos included here can familiarize you with the components of their equations and their graphs. By the time you reach the end of this chapter, you should be able to do the following:
- Identify the directrices of parabolas, hyperbolas and ellipses
- Describe the relationship between foci and directrices
- Write equations for each of these conic sections
|The Focus and Directrix of a Parabola||Learn what a focus and directrix are. Practice identifying them in the graphs of parabolas.|
|Finding the Equation of a Parabola from the Focus and Directrix||Write the equation for a parabola when given the focus and directrix.|
|Foci and the Definitions of Ellipses and Hyperbolas||Examine the distance between the foci and directrix of an ellipse. Do the same for hyperbolas.|
|Derive the Equation of an Ellipse from the Foci||Write an ellipse's equation when given coordinates for the foci.|
|Derive the Equation of a Hyperbola from the Foci||Write a hyperbola's equation when given coordinates for the foci.|
|Practice with the Conic Sections||Hone your ability to write equations and identify the graphs of hyperbolas, ellipses and parabolas.|
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.
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.
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.
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.
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.
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.
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Other chapters within the NY Regents Exam - Geometry: Test Prep & Practice course
- High School Geometry: Foundations of Geometry
- High School Geometry: Logic in Mathematics
- Introduction to Geometric Figures
- High School Geometry: Similar Polygons
- High School Geometry: Quadrilaterals
- High School Geometry: Circular Arcs and Circles
- High School Geometry: Analytical Geometry
- Triangles and Congruency
- Parallel Lines and Polygons
- Geometric Solids
- About the NY Regents Examinations
- NY Regents Exam - Geometry Flashcards