About This Chapter
Conic Sections Overview - Chapter Summary
If you have been looking for resources to help you better understand conic sections, this overview can help. Fun videos offer an in-depth look at the geometric principles of parabolas, hyperbolas and ellipses. Access these lessons anytime your schedule permits. By the end of this chapter, you will have the knowledge to:
- Identify the three main forms of a quadratic equation
- Write the equation of a parabola, hyperbola and ellipse in standard form
- Identify a conic section by its formulas
- Graph a hyperbola by using the standard equation to find the focus points, vertices and center point
- Define, create and graph ellipses
- Differentiate between standard form equations for conic sections, polar forms and parametric forms
Review these lessons in video and/or transcript formats depending on your study and learning preference. Videos are fun to watch and average about 8 minutes each, and include full transcripts. Learn more about topics covered in the lessons by submitting questions using the Ask Our Experts feature in the Dashboard. When ready, assess your comprehension by taking short lesson quizzes and a chapter exam.
1. Parabolas in Standard, Intercept, and Vertex Form
By rearranging a quadratic equation, you can end up with an infinite number of ways to express the same thing. Learn about the three main forms of a quadratic and the pros and cons of each.
2. How to Write the Equation of a Parabola in Standard Form
After watching this video lesson, you will be able to write the equation of a parabola in standard form when given just two important points from the parabola. Learn what these two points are and how they relate to the parabola.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. Conic Sections in Polar & Parametric Forms
After watching this video lesson, you will learn to distinguish between the standard form equations for conic sections, the parametric form equations and the polar form equations.
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Other chapters within the AP EAMCET E (Engineering): Study Guide & Test Prep course
- Principles of Mathematical Functions
- Mathematical Induction
- Overview of Matrices
- Overview of Complex Numbers
- Understanding Quadratic Expressions
- Theory of Equations
- Permutations & Combinations in Algebra
- Understanding the Binomial Theorem
- Understanding Partial Fractions
- Fundamental Elements of Trigonometry
- Understanding Hyperbolic Functions
- Trigonometric Properties of Triangles
- Vector Algebra
- Measures of Dispersion
- Principles of Probability
- Coordinate Geometry Overview
- Lines & Circles
- Three-Dimensional Coordinates
- Limits & Continuity
- Differentiation in Calculus
- Integration in Calculus
- Understanding Differential Equations
- Understanding the Basics of Physics
- Units & Measurement in Physics
- Understanding Motion in Physics
- Systems of Particles & Rotational Motion
- Work, Energy & Power Overview
- Overview of Oscillations
- Overview of Gravitation
- Properties of Solids, Fluids & Gases
- Thermal Properties of Matter
- Rays, Waves & Wave Optics
- Understanding Electricity
- Magnetic Force & Electromagnetism
- Currents, Waves & Circuits
- Communication Systems
- Atoms & Nuclei
- Atomic Structure Overview
- Understanding Elements & the Periodic Table
- Chemical Bonding & Molecular Structure
- States of Matter in Chemistry
- Basic Stoichiometry
- Thermodynamics & Chemistry
- Chemical Equilibrium & Acid-Bases
- Hydrogen & Hydrogen Compounds
- Alkali & Alkaline Earth Metals
- Environmental Chemistry
- Understanding Organic Chemistry
- Solids in Chemistry
- Electrochemistry & Chemical Kinetics
- Surface Chemistry
- Metallurgy Overview
- Polymers Overview
- Understanding Biomolecules
- Everyday Chemistry
- AP EAMCET E (Engineering) Flashcards