Circles

INTRODUCTION

Here are a few quick facts that are useful to know about a circle that has radius r:

      

Diameter = 2r
Circumference = 2π r
Area = πr²

Example: If a circle has an area of 16π, what is its radius?

Solution: 

A = π r² but we have A = 16π 

so  π r² = 16π

          r² = 16

            r = 4

THE EQUATION OF A CIRCLE

A circle with radius r centred at the origin has the equation:

x² + y² = r²

A circle whose centre is at the point (a,b) has the equation:

(x - a)² + (y - b)² = r²

Example: Consider the circle given by the equation (x - 3)² + (y + 2)² = 49

What is the position of it's centre? What is the radius?

Solution:

The centre is at (3, -2).

The radius is 7.