About This Chapter
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
|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.|
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.
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.
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.
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.
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.
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.
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Other chapters within the Geometry: High School course
- High School Geometry: Foundations of Geometry
- High School Geometry: Logic in Mathematics
- High School Geometry: Introduction to Geometric Figures
- High School Geometry: Properties of Triangles
- High School Geometry: Triangles, Theorems and Proofs
- High School Geometry: Parallel Lines and Polygons
- High School Geometry: Similar Polygons
- High School Geometry: Quadrilaterals
- High School Geometry: Circular Arcs and Circles
- High School Geometry: Geometric Solids
- High School Geometry: Analytical Geometry
- High School Geometry: Probability
- High School Geometry: Introduction to Trigonometry