# Ch 34: CEOE Middle Level/Intermediate Math: Conic Sections

### About This Chapter

## CEOE Middle Level/Intermediate Math: Conic Sections - Chapter Summary

Use the lessons in this chapter before taking the CEOE Middle Level/Intermediate Math test. In addition to being a confidence builder, they will help you answer test questions having to do with the material the lessons cover, including:

- Getting familiar with the focus and directrix elements of a parabola
- Working out the equation of a parabola using the focus and directrix
- Understanding the definitions of an ellipse and a hyperbola in relation to foci
- Working out the equation of an ellipse and a hyperbola by using the foci
- How to discover the equation for a circle
- Practice problems for conic sections

These lessons break up the subject matter into short sections that focus on one concept at a time. We quiz you on the material to validate that you understand what was just discussed. Also, there is a feature that allows you to ask a question of an expert.

### 1. 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.

### 2. 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.

### 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. How to Find the Equation of a Circle

There are two commonly used forms of equations for a circle, in this lesson we'll take a few minutes to examine and understand both forms, and be able to convert from one to the other.

### 7. 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

Other chapters within the OSAT Middle Level/Intermediate Mathematics (CEOE) (125): Practice & Study Guide course

- CEOE Middle Level/Intermediate Math: Problem Solving Strategies
- CEOE Middle Level/Intermediate Math: Reasoning & Logic
- CEOE Middle Level/Intermediate Math: Mathematical Modeling
- CEOE Middle Level/Intermediate Math: Real Numbers
- CEOE Middle Level/Intermediate Math: Fractions
- CEOE Middle Level/Intermediate Math: Decimals
- CEOE Middle Level/Intermediate Math: Percentages
- CEOE Middle Level/Intermediate Math: Ratios, Rates & Proportions
- CEOE Middle Level/Intermediate Math: Exponents & Exponential Expressions
- CEOE Middle Level/Intermediate Math: Properties of Real Numbers
- CEOE Middle Level/Intermediate Math: Sequences & Series
- CEOE Middle Level/Intermediate Math: Introduction to Algebra
- CEOE Middle Level/Intermediate Math: Introduction to Functions
- CEOE Middle Level/Intermediate Math: Linear Equations
- CEOE Middle Level/Intermediate Math: Linear Inequalities
- CEOE Middle Level/Intermediate Math: Systems of Equations
- CEOE Middle Level/Intermediate Math: Matrices in Linear Algebra
- CEOE Middle Level/Intermediate Math: Quadratic Functions
- CEOE Middle Level/Intermediate Math: Polynomial Functions
- CEOE Middle Level/Intermediate Math: Rational Expressions
- CEOE Middle Level/Intermediate Math: Radical Expressions
- CEOE Middle Level/Intermediate Math: Absolute Value Functions
- CEOE Middle Level/Intermediate Math: Exponential & Logarithmic Equations
- CEOE Middle Level/Intermediate Math: Measurement
- CEOE Middle Level/Intermediate Math: Area & Perimeter
- CEOE Middle Level/Intermediate Math: Surface Area & Volume
- CEOE Middle Level/Intermediate Math: Foundations of Geometry
- CEOE Middle Level/Intermediate Math: Lines & Angles
- CEOE Middle Level/Intermediate Math: Properties of Triangles
- CEOE Middle Level/Intermediate Math: Similar & Congruent Triangle Proofs
- CEOE Middle Level/Intermediate Math: Right Triangle Proofs
- CEOE Middle Level/Intermediate Math: Quadrilaterals & Polygons
- CEOE Middle Level/Intermediate Math: Circles & Arc of a Circle
- CEOE Middle Level/Intermediate Math: Coordinate Geometry
- CEOE Middle Level/Intermediate Math: Transformations in Geometry
- CEOE Middle Level/Intermediate Math: Trigonometry
- CEOE Middle Level/Intermediate Math: Limits
- CEOE Middle Level/Intermediate Math: Rate of Change & Derivatives
- CEOE Middle Level/Intermediate Math: Area Under the Curve & Integrals
- CEOE Middle Level/Intermediate Math: Probability
- CEOE Middle Level/Intermediate Math: Discrete Probability Distributions
- CEOE Middle Level/Intermediate Math: Continuous Probability Distributions
- CEOE Middle Level/Intermediate Math: Overview of Statistics
- CEOE Middle Level/Intermediate Math: Sampling
- CEOE Middle Level/Intermediate Math: Graphs, Charts & Diagrams
- CEOE Middle Level/Intermediate Math: Summarizing Data
- CEOE Middle Level/Intermediate Math: Discrete Mathematics
- OSAT Middle Level/Intermediate Mathematics (CEOE) (125) Flashcards