# Ch 40: ORELA Math: Conic Sections

### About This Chapter

## ORELA Mathematics: Conic Sections - Chapter Summary

As part of your preparation for the for the ORELA Mathematics exam, use these lesson videos to learn more about conic sections. Watch our expert instructors as they explain the properties of a parabola, ellipses, hyperbolas and foci. Once you finish the lessons, you could be prepared to answer questions about:

- Focus, directrix and equations of a parabola
- Foci of ellipses and hyperbolas
- Equations for ellipse and hyperbolas from the foci

If you think you would benefit from an alternative review of the material, try reading over the lesson transcripts which present the same material in a written format. Complete the chapter by working on lesson worksheets and quizzes.

### ORELA Mathematics: Conic Sections Objectives

Individuals take the ORELA Mathematics exam to demonstrate their expertise in the field of mathematics and become certified math teachers. This computerized certification exam is used by the state of Oregon and has a time limit of 4 hours and 15 minutes. There are 150 multiple-choice questions on it, and about 19% are about measurements and geometry. Use the tools of this chapter to prepare for questions in the Measurements and Geometry content domain on the properties of conic sections.

### 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.

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### Other Chapters

Other chapters within the ORELA Mathematics: Practice & Study Guide course

- ORELA Math: Properties of Real Numbers
- ORELA Math: Fractions
- ORELA Math: Decimals & Percents
- ORELA Math: Ratios & Proportions
- ORELA Math: Units of Measure & Conversions
- ORELA Math: Logic
- ORELA Math: Reasoning
- ORELA Math: Vector Operations
- ORELA Math: Matrix Operations & Determinants
- ORELA Math: Exponents & Exponential Expressions
- ORELA Math: Algebraic Expressions
- ORELA Math: Linear Equations
- ORELA Math: Inequalities
- ORELA Math: Absolute Value
- ORELA Math: Quadratic Equations
- ORELA Math: Polynomials
- ORELA Math: Rational Expressions
- ORELA Math: Radical Expressions
- ORELA Math: Systems of Equations
- ORELA Math: Complex Numbers
- ORELA Math: Functions
- ORELA Math: Piecewise Functions
- ORELA Math: Exponential & Logarithmic Functions
- ORELA Math: Continuity of a Function
- ORELA Math: Limits
- ORELA Math: Rate of Change
- ORELA Math: Calculating Derivatives & Derivative Rules
- ORELA Math: Graphing Derivatives
- ORELA Math: Applications of Derivatives
- ORELA Math: Area Under the Curve & Integrals
- ORELA Math: Integration Techniques
- ORELA Math: Applications of Integration
- ORELA Math: Foundations of Geometry
- ORELA Math: Geometric Figures
- ORELA Math: Properties of Triangles
- ORELA Math: Triangle Theorems & Proofs
- ORELA Math: Parallel Lines & Polygons
- ORELA Math: Quadrilaterals
- ORELA Math: Circles & Arc of a Circle
- ORELA Math: Geometric Solids
- ORELA Math: Analytical Geometry
- ORELA Math: Trigonometric Functions
- ORELA Math: Trigonometric Graphs
- ORELA Math: Solving Trigonometric Equations
- ORELA Math: Trigonometric Identities
- ORELA Math: Sequences & Series
- ORELA Math: Graph Theory
- ORELA Math: Set Theory
- ORELA Math: Statistics Overview
- ORELA Math: Summarizing Data
- ORELA Math: Tables, Plots & Graphs
- ORELA Math: Probability
- ORELA Math: Discrete Probability Distributions
- ORELA Math: Continuous Probability Distributions
- ORELA Math: Sampling
- ORELA Math: Regression & Correlation
- ORELA Mathematics Flashcards