About This Chapter
Who's it for?
This unit of our High School Geometry Homeschool course will benefit any student who is trying to learn about conic sections. There is no faster or easier way to learn about focus and directrix. Among those who would benefit are:
- Students who require an efficient, self-paced course of study to learn how to derive equations of parabolas, hyperbolas and ellipses.
- Homeschool parents looking to spend less time preparing lessons and more time teaching.
- Homeschool parents who need a math curriculum that appeals to multiple learning types (visual or auditory).
- Gifted students and students with learning differences.
How it works:
- Students watch a short, fun video lesson that covers a specific unit topic.
- Students and parents can refer to the video transcripts to reinforce learning.
- Short quizzes and the Focus and Directrix unit exam confirm understanding or identify any topics that require review.
Focus and Directrix Unit Objectives:
- Use the focus and directrix to find the equation of a parabola.
- Calculate the equation of an ellipsis from the foci.
- Use the foci to derive the equation of a hyperbola.
- Practice working with a conic section.
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 High School Geometry: Homeschool Curriculum course
- Foundations of Geometry: Homeschool Curriculum
- Logic in Mathematics: Homeschool Curriculum
- Geometric Figures: Homeschool Curriculum
- Properties of Triangles: Homeschool Curriculum
- Triangles, Theorems & Proofs: Homeschool Curriculum
- Parallel Lines & Polygons: Homeschool Curriculum
- Similar Polygons: Homeschool Curriculum
- Quadrilaterals: Homeschool Curriculum
- Circular Arcs and Circles: Homeschool Curriculum
- Geometric Solids: Homeschool Curriculum
- Analytical Geometry: Homeschool Curriculum
- Introduction to Trigonometry: Homeschool Curriculum