About This Chapter
The Ellipse in Algebra - Chapter Summary
This informative chapter covers ellipses in algebra, including how they are defined and graphed. You'll learn how to find the major axis of an ellipse and the points and coordinates on an ellipses graph. Other topics include the focal lengths and chords of ellipses. Once you finish the lessons in this chapter, you should be ready to:
- Use the foci to derive the equation of an ellipse
- Differentiate between the tangent and normal lines of an ellipse
- Write the equation of an ellipse in standard form
- Explain the reflective properties of ellipses
Let our informative chapter help you get ready for a test or complete a homework assignment. Each video or text lesson is followed by a short multiple-choice quiz that makes a great test prep exercise. If you need any help as you complete the lessons, ask one of our instructors for assistance. Feel free to access these study tools 24 hours a day on your computer, mobile phone or tablet.
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 Find the Major Axis of an Ellipse
In this lesson, we'll review the definition of an ellipse, learn how to find the major axis of an ellipse given the foci and one point on the ellipse, and look at an application of this process.
3. 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.
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. Reflective Properties of Ellipses
This lesson will review ellipses. We will then explore a fascinating property of ellipses called the reflective property of an ellipse. We will see how this can apply in a given scenario, and we will explain why it is true.
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Other chapters within the HSC Mathematics: Exam Prep & Syllabus course
- Mathematical Proofs & Reasoning
- Basic Arithmetic & Algebra
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Plane Geometry
- Circle Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Geometrical Representations of Functions
- Linear Functions & Lines
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Geometrical Applications of Differentiation
- Logarithmic & Exponential Functions
- Calculating Trigonometric Functions
- Understanding Inverse Functions
- Factoring & Graphing Polynomials
- Roots & Coefficients of Polynomials
- Binomial Theorem & Probability
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Geometric Representations of Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Rate of Change
- Calculus Applications: Velocity & Acceleration
- Calculus Applications: Projectile & Harmonic Motion
- Calculus Applications: Resisted Motion
- Calculus Applications: Circular Motion
- HSC Mathematics Flashcards