About This Chapter
Analytic Geometry - Chapter Summary
Our instructors will define a dihedral angle, teach you how to graph points and lines in three dimensions and find the equation for a circle. You will learn the definition and formulas associated with spheres and how foci relate to ellipses and hyperbolas.
Your study will continue with a differentiation between the polar forms and parametric forms of conic sections and a study of the angle formed from two intersecting lines. Given three points, you will also learn how to find the equation of a plane. This chapter will prepare you to do the following:
- Calculate dihedral angles
- Use a formula to find the distance between a point and a line
- Graph in three dimensions
- Understand two commonly used formulas for the equation of a circle
- Define ellipsis and hyperbola
- Extend the Pythagorean theorem to find the distance between two points in three-dimensional space
- Explain what cosines and ratios are
Our lessons and quizzes are accessible to you 24 hours a day, seven days a week. Use the quizzes and chapter tests to gauge how well you understand the material. Each lesson is accompanied by a printable transcript so you can review the material offline at any time. If you have questions as you work through the chapters, contact one of our instructors for more help.
1. Dihedral Angle: Definition & Calculation
Dihedral angles show up frequently in the world around us. Through definition and example, we will learn what a dihedral angle is and how to calculate it. After you finish the lesson, you can test your new-found knowledge with a quiz!
2. How to Find the Distance Between a Point & a Line
Finding the distance from a point to a line is useful in many science and engineering applications. In this lesson, we calculate this distance using a formula, as well as with some fundamental concepts from geometry and algebra.
3. Graphing Points & Lines in Three Dimensions
After watching this video lesson, you will know how read the three coordinates given to you and graph any given point in the three-dimensional coordinate space. Then test your knowledge with a quiz.
4. How to Find the Equation of a Circle
There are two commonly used forms of equations for a circle, in this lesson we'll take a few minutes to examine and understand both forms, and be able to convert from one to the other.
5. Sphere: Definition & Formulas
A sphere is a perfectly round three-dimensional object. This lesson will give a mathematical definition of a sphere, discuss the formulas associated with spheres and finish with a quiz.
6. 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.
7. 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.
8. Calculating the Angle Formed From Intersecting Lines
In this lesson, you'll learn a different way of finding an angle between two intersecting lines. This method is useful when you know only the slopes of the lines.
9. Finding the Distance Between Two Points in a Three Dimensional Space
In this lesson we use Pythagoras' theorem and right triangles to develop an equation to find the distance between any two points in a three-dimensional space.
10. Direction Cosines & Ratios: Definition & Calculations
Direction cosines and ratios are a way to represent the direction of a 3D vector. In this lesson, learn how to calculate and understand direction cosines and ratios.
11. Finding the Equation of a Plane from Three Points
In this lesson we will learn the technique for computing the equation of a plane when the coordinates of three noncollinear points in three dimensional space are given.
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Other chapters within the NDA Exam Preparation & Study Guide course
- About the NDA Exam
- Algebra Concepts
- Advanced Algebra Concepts
- Solving Matrices & Determinants
- Trigonometry Concepts
- Geometry & Linear Equations
- Functions, Limits & Continuity
- Derivative Rules
- Calculations & Applications of Derivatives
- Integral Calculus
- Differential Equations & Applications
- Scalars & Vectors in Algebra
- Visualizing Statistics
- Probability Concepts in Math
- Grammar and Usage
- Improving Reading Comprehension
- Measurements in Physics
- Motion in Physics
- Basics of Work, Power & Energy
- Understanding Heat Transfer
- Sound Waves
- Light, Mirrors & Lenses
- Electric Currents & Power
- Scientific Technology, Machines & Tools
- The Atom & Structure of Elements
- Chemical Properties of Elements & Substances
- Chemical Symbols, Formulas & Reactions
- Qualities of Living Organisms
- Health Science Basics
- Solar System & Eclipses
- Achievements of Famous Scientists
- Indian History
- Overview of Major World History Events
- World Government Types
- The Earth
- Earth's Oceans, Atmosphere & Climate
- Regional Geography of South Asia
- Modern Day Events in India
- NDA Exam Preparation & Study Guide Flashcards