About This Chapter
Who's it for?
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- Have fallen behind in understanding how to derive equations for parabolas and other conic sections.
- Need an efficient way to learn about conic sections.
- Learn best with engaging auditory and visual tools.
- Struggle with learning disabilities or learning differences, including autism and ADHD.
- Experience difficulty understanding your teachers.
- Missed class time and need to catch up.
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How it works:
- Start at the beginning, or identify the topics that you need help with.
- Watch and learn from fun videos, reviewing as needed.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Submit questions to one of our instructors for personalized support if you need extra help.
- Verify you're ready by completing the Conic Sections chapter exam.
Why it works:
- Study Efficiently: Skip what you know, review what you don't.
- Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
- Be Ready on Test Day: Use the Conic Sections chapter exam to be prepared.
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Students will review:
In this chapter, you'll learn the answers to questions including:
- When given the directrix and focus, how do you find the equation for a parabola?
- What are ellipses and hyperbolas?
- When provided with the foci, how do you calculate the equation of an ellipses?
- How do you find the equation of a hyperbola when given the foci?
1. Derive the Equation of a Hyperbola from the Foci
A hyperbola can be shaped on a graph similar to a butterfly's wing and has a formula derived from the foci, which are two points inside the branches at a fixed distance from the center, and other points. Learn how to derive the equation of a hyperbola from just the foci through practice examples.
2. Derive the Equation of an Ellipse from the Foci
An ellipse refers to all points in a set where the sum of distances from the foci or two fixed points is constant. Study the definition of an ellipse and foci, and learn how to derive an equation from the horizontal and vertical major axis.
3. Finding the Equation of a Parabola from the Focus and Directrix
The equation for a parabola curve can be found from the focus and directrix. Discover how to find the standard form of the parabola equation from the focus and directrix, as well as two other forms of the equation: intercept form and vertex form.
4. Foci and the Definitions of Ellipses and Hyperbolas
Foci are points located on the curves of ellipses and hyperbolas. Study the definition of ellipses and hyperbolas, learn the foci of these shapes, and have a look at examples for further understanding.
5. Practice with the Conic Sections
Conic sections are shapes made cutting a 3D cone at specific angles. Get some practice with the conic sections by looking at examples which include circles, ellipses, parabolas, and hyperbolas.
6. The Focus and Directrix of a Parabola
A parabola is the curve of a line on the graph representing the quadratic equation, shaped like a 'U'. Learn how the focus and the directrix help define the parabola through examples with visual representations.
7. Ellipse: Definition, Equation & Examples
An ellipse is a closed curve that is identified by its foci and its stretched shape along its principal axis. Explore the definition and equation of an ellipse, and practice some example problems.
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Other chapters within the High School Geometry: Help and Review course
- Foundations of Geometry: Help and Review
- Logic in Mathematics: Help and Review
- Introduction to Geometric Figures: Help and Review
- Properties of Triangles: Help and Review
- Triangles, Theorems and Proofs: Help and Review
- Parallel Lines and Polygons: Help and Review
- Similar Polygons: Help and Review
- Quadrilaterals: Help and Review
- Circular Arcs and Circles: Help and Review
- Geometric Solids: Help and Review
- Analytical Geometry: Help and Review
- Introduction to Trigonometry: Help and Review
- Constructing Geometric Figures