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.