# Ch 40: NMTA Math: Conic Sections

### About This Chapter

## NMTA Math: Conic Sections - Chapter Summary

Use the online video lessons in this chapter to explore and review the fundamentals of working with conic sections. While studying this chapter, you'll be re-introduced to various types of conic sections as well as their properties. The lessons also ensure that you know the correct ways to construct them. Watching the lessons might enhance your performance on the NMTA examination. Look to these online videos for help with:

- Understanding a parabola's focus and directrix
- Using the focus and directrix to calculate the equation of a parabola
- Describing ellipses, foci and hyperbolas
- Utilizing the foci to derive the equations of hyperbolas and ellipses

You'll explore these and other concepts when you view this chapter's online video lessons. As a candidate for the NMTA Math examination, you'll benefit from the experience of the credentialed instructors who can answer your submitted questions on conic sections. Use the written transcripts or the video tags to review or clarify any of the information. Test your knowledge with the self-assessment quizzes and the chapter examination.

### NMTA Math: Conic Sections Chapter Objectives

The topics you will study in this chapter on conic sections will also be covered in the Measurement and Geometry section of the NMTA Math examination. This third section of the five-part examination amounts to 19% of the entire score. Your ability to understand and analyze conic sections and other mathematical principles will be evaluated. You'll be given four hours and 15 minutes to answer 150 multiple-choice questions on the computer-based examination.

### 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 NMTA Mathematics (304): Practice & Study Guide course

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