About This Chapter
Honors Geometry: Conic Sections - Chapter Summary and Learning Objectives
Take advantage of resources in this chapter to complete homework assignments and successfully pass quizzes and tests that focus on conic sections. Entertaining lessons make it easy for you to understand this subject area by providing in-depth looks at a variety of concepts, including how to identify a conic section, and learn the meaning of the parabola, ellipses and hyperbolas.
Navigate the lessons with ease by selecting the first one in this chapter to review then scrolling along the right-hand side bar to choose others in any sequence you desire. Revisit them as often as needed until you feel confident that you fully understand conic sections. Also, take short quizzes and a chapter exam to gauge your comprehension of the lessons. Upon completion of this chapter, you will understand:
- Ways to identify a conic section by its formulas
- The meaning of a parabola
- Foci and the meaning of ellipses and hyperbolas
- How to derive the equation of an ellipse and hyperbola from the foci
|How to Identify a Conic Section by Its Formulas||Study how to distinguish between the many formulas of a conic section.|
|What is a Parabola?||Learn the definition of a parabola, where to find it in real life and the correct vocabulary to use when talking about it.|
|Foci and the Definitions of Ellipses and Hyperbolas||Examine foci and the meaning of ellipses and hyperbolas.|
|Derive the Equation of an Ellipse from the Foci||Understand how to derive the equation of an ellipse from the foci.|
|Derive the Equation of a Hyperbola from the Foci||Discover the process of deriving the equation of a hyperbola from the foci.|
|Practice with the Conic Sections||Demonstrate your ability to complete practice questions with conic sections.|
1. How to Identify a Conic Section by Its Formulas
In algebra, we have a formula for everything. Take a cone and slice it and we have a formula for the shape that results. Watch this video lesson to learn how to distinguish between these formulas.
2. What is a Parabola?
When you see a U shape in a graph, that is called a parabola. Learn more about what a parabola is, its characteristics, and the differences between concave-up and concave-down parabolas.
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 Honors Geometry Textbook course
- Honors Geometry: Foundations of Geometry
- Honors Geometry: Fundamentals of Geometry Proofs
- Honors Geometry: Logic in Mathematics
- Honors Geometry: Introduction to Geometric Figures
- Honors Geometry: Properties of Triangles
- Honors Geometry: Similar & Congruent Triangle Proofs
- Honors Geometry: Right Triangle Proofs
- Honors Geometry: Relationships Within Triangles
- Honors Geometry: Parallel Lines & Polygons
- Honors Geometry: Parallel Line Proofs
- Honors Geometry: Coordinate Geometry
- Honors Geometry: Analytical Geometry
- Honors Geometry: Similar Polygons
- Honors Geometry: Properties of Polygons & Circles
- Honors Geometry: Polygons & Quadrilaterals
- Honors Geometry: Circular Arcs & Circles
- High School Geometry: Geometric Solids
- Honors Geometry: Introduction to Trigonometry
- Honors Geometry: Right Triangles & Trigonometry
- Honors Geometry: Area, Surface Area & Volume
- Honors Geometry: Perimeter & Circumference
- Honors Geometry: Transformations
- Honors Geometry: Matrices