-5
9.3
Circles:
Parts of a circle:
Standard form of a circle: x
2  y
2  r
2
Name:
Where r is the radius and the center is at (0,0)
Example 1:
Find the radius and graph the circle. x
2  y
2 
16 5
Example 2:
Find the radius and write an equation of the circle.
Assignment:
Find the radius and graph the circle.
1. x
2  y
2 
100 2. x 2  y 2 
4
9
5 5
-5
-5
-5
5
-5
3.
5 x
2  y
5
2 
5
20
5 -5 5 -5
-5 -5 -5
5

4. Write the equation of a circle whose center is at (0,0) and had a radius 7.
Draw a speed graph.
5. Find the radius and write the equation of the circle.
5
-5 5
-5
Bored yet? I am how about we move the circle?
-5
5
-5
Standard form of a circle not centered at the origin.
 x
 h
  y
 k

2  r
2
Where r is the radius and the center is at ( h,k )
Example 3:
Find the radius, the center and graph the circle.
 x

2
  y

1

2 
9
5
Example 4:
Find the radius, the center and write an equation of the circle.
-5
-5
5
-5
-5
Example 5:
A circle has a radius of 12 and is centered at (-4,10). Write its equation.
5
5
5

Homework:
Write an equation for the circle with the given center and radius.
1. Center: (1,-3) Radius: 10 2. Center: (-5,-1) Radius: 6
For each equation find the center and the radius.
3.
 x

1
  y

4

2 
1 4.
 x

3
  y

1

2 
36
Find the center and the radius and then graph the circle.
6.
 x

9
  y

2

2 
100 7.
 x

3
  y

9

2 
49
For each graph give the center and the radius and write the equation.
10. y
11. y
-5
5
-5
5 x
-5
5
-5
5. x
2   y

3

2 
25
9.
 x

6

2  y
2 
64
5 x