About This Chapter
Conic Sections in Coordinate Geometry - Chapter Summary
Our engaging chapter introduces you to the concept of a parabola, the focus and directrix of a parabola and some examples of both. These lessons cover the processes of deciphering the equation for an ellipse from the foci and graphing an ellipse using algebra.
You'll also learn how to graph a hyperbola using the standard equation to locate the focus points, vertices and center point. Once you finish this chapter, you should be ready to:
- Identify several equations used for the parabola
- Define ellipse and hyperbola
- Decipher information about an ellipse from its equation
- Write the standard form equation of a hyperbola
- Use formulas to identify a conic section
Test your knowledge of this subject by taking the multiple-choice lesson quizzes and chapter test ahead of a big exam or project. Fill in any gaps where you need to review the material further by watching our video lessons and reading through the text lessons. You don't need to watch an entire video lesson if you don't need to. Simply use the video tabs feature in the Timeline to jump ahead to the section that you need to focus on.
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. 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.
6. 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.
7. 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.
8. 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.
9. 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 within the BITSAT Exam - Math: Study Guide & Test Prep course
- Expressions & Reasoning in Math
- Complex Numbers & Polynomials in Algebra
- Introduction to Quadratics
- Working with Quadratic Functions Overview
- Mathematical Sequences & Series Overview
- Series & Sequences Application
- Exponential Functions & Logarithmic Equations
- Binomial Theorem Overview
- Overview of Matrices & Determinants
- Sets & Relations in Math
- Introduction to Trigonometric Functions
- Trigonometric Identities Overview
- Real World Trigonometric Applications
- Operating with Functions
- Solving Inequalities
- Two-Dimensional Coordinate Geometry
- Straight Lines & Angles in Coordinate Geometry
- Circular Arc & Circles in Coordinate Geometry
- Three-Dimensional Coordinate Geometry
- Limits & Continuity in Differential Calculus
- Calculating Derivatives
- Differentiable Functions & Min-Max Problems
- Differentiability in Integral Calculus
- Overview of Probability in Calculus
- Vectors & Scalars in Math
- Dispersion & Frequency Distributions in Statistics
- Linear Programming & Systems of Equations
- Definite Integrals
- Permutation & Combination
- Mathematical Modeling Overview
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