# Ch 23: Analytic Geometry and Conic Sections

### About This Chapter

## Analytic Geometry and Conic Sections - Chapter Summary and Learning Objectives

Conic sections, otherwise known as circles, ellipses, hyperbolas and parabolas, are the shapes you get when you cut a slice through two cones. Use the lessons included in this chapter to explore their basic characteristics and investigate the relationship between their foci and vertices, so you can graph and solve equations for conic sections with ease. Once you work your way through this chapter, you should be able to:

- Write the equations for conic sections in standard form
- Graph ellipses, hyperbolas and parabolas
- Calculate the distance of a circle

Video | Objectives |
---|---|

Defining and Graphing Ellipses in Algebra | Learn what an ellipse is. Find out how to graph ellipses centered at the origin and at other points on the coordinate plane. |

How to Write the Equation of an Ellipse in Standard Form | Check out the standard form of an ellipse's equation and learn how to write it. |

The Circle: Definition, Conic Sections & Distance Formula | Consider the definition of a circle and get an introduction to conic sections. Discover the formula used to calculate a circle's distance. |

The Hyperbola: Definition, Vertices, Foci & Graphing | Learn how to locate a parabola's foci and vertices. Graph hyperbolas centered at the origin and at other points on the coordinate plane. |

How to Write the Equation of a Hyperbola in Standard Form | Find out how to write the equation for a hyperbola in standard form. |

The Parabola: Definition & Graphing | Understand the definition of a parabola. Learn how to graph parabolas with vertices at various points on the coordinate plane, including the origin. |

How to Write the Equation of a Parabola in Standard Form | Get tips for writing the equation of a parabola in standard form. |

How to Identify a Conic Section by Its Formulas | Use your knowledge of conic sections to identify parabolas, hyperbolas and ellipses by their formulas. |

### 1. Defining and Graphing Ellipses in Algebra

Watch this video lesson to find out what makes ellipses so unique. Learn what kind of shape an ellipse is, how you can create one yourself and how you can graph an ellipse by just looking at the numbers in the equation.

### 2. How to Write the Equation of an Ellipse in Standard Form

In algebra, we have equations that make our life so much easier. Some equations are able to tell us information without hard math. Watch this video lesson to see how the equation of an ellipse does this.

### 3. The Circle: Definition, Conic Sections & Distance Formula

Watch this video lesson, and you will learn what makes a circle a conic section. Also learn how to calculate the circumference of a circle. You will learn about the one important measurement that you need for any circle.

### 4. The Hyperbola: Definition, Vertices, Foci & Graphing

In this video lesson, we'll learn what a hyperbola is and how to graph one using the standard equation to find the center point, vertices and focus points.

### 5. How to Write the Equation of a Hyperbola in Standard Form

When it comes to equations in algebra, there is most always a standard form that provides us with useful information. Watch this video lesson to learn how to write the standard form equation of a hyperbola by using information about the hyperbola.

### 6. The Parabola: Definition & Graphing

Watch this video lesson to learn what a parabola is and how you can graph it. Find out how to extract useful information from the standard form equation of a parabola to help you graph it.

### 7. How to Write the Equation of a Parabola in Standard Form

After watching this video lesson, you will be able to write the equation of a parabola in standard form when given just two important points from the parabola. Learn what these two points are and how they relate to the parabola.

### 8. 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.

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### Other Chapters

Other chapters within the Precalculus: High School course

- Working With Inequalities
- Absolute Value Equations
- Working with Complex Numbers
- Introduction to Quadratics
- Working with Quadratic Functions
- Basics of Polynomial Functions
- Working with Higher-Degree Polynomials
- Graphing Piecewise Functions
- Understanding Function Operations
- Graph Symmetry
- Graphing with Functions
- Rate of Change
- Rational Functions & Difference Quotients
- Rational Expressions and Function Graphs
- Exponential Functions & Logarithmic Functions
- Using Trigonometric Functions
- Trigonometric Graphs
- Trigonometric Applications
- Solving Trigonometric Identities
- Vectors, Matrices and Determinants
- Mathematical Sequences and Series
- Sets in Algebra
- Polar Coordinates and Parameterizations
- Continuity
- Limits
- Teacher Resources for Precalculus in High School