Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

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Course: College Algebra
Topic: Basic Geometry
Subtopic: Circles

Overview

A circle is the two-dimensional shape formed by connecting all the points that lie at a fixed distance from a given central point. A circle is a basic geometrical object with many practical uses and mathematical history.

Equation of a circle with center (h,k) and radius r: (x-h)^2+(y-k)^2=r^2

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 6.2.1 Understand the standard equation of a circle and how to find from it the center (h,k) and radius (r) of the circle
• 6.2.2 Given the graph of a circle or information about the graph, find the equation of the circle in standard form
• 6.2.3 Algebraically convert the general form of a circle to the standard form by completing the square as needed
• 6.2.4 Given the equation of a circle, produce its graph both manually and electronically
• 6.2.5 Know how the constant pi (pi) relates to a circle, that pi is an irrational number, and the decimal approximation of pi to five decimal places
• 6.2.6 Know and be able to use the formulas for the circumference of a circle and the area of a circle
• 6.2.7 Know that the tangent line to a circle is perpendicular to its radius and why

Terminology

Terms you should be able to define: circle, center, radius, diameter, circumference C=piD, area A=pir^2, standard form (x-h)^2+(y-k)^2=r^2, general form y=ax^2+bx+cy^2+dy+e, chord of a circle, tangent line to a circle

Mini-Lectures and Examples

Supplementary Resources (recommended)

A fun read: Quite Interesting Facts About Circles from The Telegraph in the U.K.

Supplemental Resources (optional)

If you need supplemental tutorial videos with examples relevant to this section go to James Sousa's MathIsPower4U and search for topics: "Graphing and Writing Equations of Circles"

rev. 2020-10-10