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 (π) 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**

Define: circle, center, radius, diameter, circumference C=πD, area A=πr^{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

**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"