# Chapter 6: Analyzing Conic Sections

**At Grade**Created by: CK-12

## Introduction

"Conic Section" is a general term for the class of shapes formed by slicing through an infinite 3-dimensional cone in different ways and looking at the resulting "face." Each of the shapes results in a section of the original cone, hence the name.

Conic sections include: ellipses, circles, parabolas, and hyperbolas (formed using two cones point-to-point). The chapter also introduces the "Dandelin Spheres," a beautifully simple physical representation of various rules governing conic sections.

By the time you reach the end of this chapter, you should have a much deeper understanding of the applications of conic sections and the calculations that define them.

- 6.1.
## Equation of an Ellipse

- 6.2.
## Focal Property of Ellipses

- 6.3.
## Parabolas and the Distance Formula

- 6.4.
## Parabolas and Analytic Geometry

- 6.5.
## Applications of Parabolas

- 6.6.
## Hyperbola Equations and the Focal Property

- 6.7.
## Hyperbolas and Asymptotes

- 6.8.
## Conic Sections and Dandelin Spheres

- 6.9.
## General Forms of Conic Sections

### Chapter Summary

## Summary

This chapter on conic section analysis covers all of the classes of conics, and includes a review of the associated calculations.

Dandelin Spheres are introduced and the proofs of the focus properties and definitions of associated vocabulary are discussed.

Students are expected to understand the similarities and differences between ellipses, parabolas and hyperbolas, and should recognize the similarities and differences between the various ways in which each shape is related to its foci, directrix, vertex, etc.

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