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Equation of a Circle: Introduction

Equation of a Circle: Introduction

Author: Alex G
Description:

After completing this packet you should be able to:
* Write the equation of a circle centered at the origin
* Understand the derivation of the equation for a circle
* Write the equation of a circle given the coordinates of its center and the radius of the circle.
* Write the equation of a circle given the coordinates of its center and a point on the circle.
* Find the center and radius of a circle given its equation in standard form

This packet uses a video with three examples to demonstrate the derivation of a the equation for a circle centered at the origin. After watching the video, you should be able to complete the first set of practice problems.

The second video shows the derivation of the equation for a circle in standard form for a circle not centered at the origin. The packet includes a second set of practice problems. Make sure you complete the problems so you know that you have mastered the concepts!

Cover art for this packet was taken from the Morgue File website at http://www.morguefile.com/. Morgue File allows use of its images for creative work.

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Tutorial

Introduction: Derivation of the Equation for a Circle at the Origin

Watch this video and then try the Practice Problems below!

Example Problems of Circles Centered at the Origin

Three problems of equations of circles with center at (0,0). Master these before moving on to the video about circles centered anywhere on the plane.

Source: Graphs created using tools from http://geogebra.org

Lesson: Equation of a Circle Centered Anywhere on the Plane

Covers the development of the equation for a circle centered anywhere in the plane and works through three example problems.

Practice Problems

Includes three examples of circles centered somewhere other than the origin.

Do you want more?

Sometimes you are given an equation for a circle that is not in standard form, and you have to use completing the square before you can find the center and the radius of the circle.  This concept is generally not expected in an introductory geometry course, but it might be in an enirched class, or you might find it in precalculus.

Completing the square to find the center and the radius of a circle can be found in my packet "Equation of a Circle: Advanced Topics".