2. Definition of a Circle
A circle is a set of points a given distance
from one point called the center.
The distance from the center is called the
radius
3. Standard equation of the circle
If the circle is at the origin
x 2 + y 2 = r 2 r is the radius
If the circle is not at the origin
The center is at (h, k)
2
2
2
r
k
y
h
x
4. Standard equation of the circle
If the circle is at the origin
x 2 + y 2 = r 2 r is the radius
If the circle is not at the origin
Solve for r
2
2
2
r
k
y
h
x
2
2
k
y
h
x
r
5. Write the equation of Circle
Center at ( -5,0) and radius 4.8
h =?
k =?
r = 4.8
2
2
2
r
k
y
h
x
6. Write the equation of Circle
Center at ( -5,0) and radius 4.8
h =-5
k =0
r = 4.8
2
2
2
r
k
y
h
x
04
.
23
5
8
.
4
0
5
2
2
2
2
2
y
x
y
x
7. Write the equation of Circle
Center at ( 4, -3) and
a point on the circle (2,1)
h =
k =
r =
x =
y =
2
2
2
r
k
y
h
x
8. Write the equation of Circle
Center at ( 4, -3) and
a point on the circle (2,1)
h = 4
k = - 3
r =
x = 2
y = 1
2
2
2
r
k
y
h
x
20
16
4
4
2
3
1
4
2
2
2
2
2
2
2
2
r
r
r
9. Write the equation of Circle
Center at ( 4, -3) and
a point on the circle (2,1)
h = 4
k = - 3
r2 = 20
x = 2
y = 1
2
2
2
r
k
y
h
x
20
3
4
20
3
4
2
2
2
2
y
x
y
x
10. Given the equation of the Circle
(x – 13)2 + (y – 6)2 = 52
Tell if the point is inside or outside the circle.
(5, 6)
11. Given the equation of the Circle
(x – 13)2 + (y – 6)2 = 52
Tell if the point is inside or outside the circle.
(5, 6) (5 -13)2 + (6 – 6)2 is it <, >, or = 52
( - 8)2 + 02 = 64 = 25
Greater then outside the circle.
Less then Inside the circle.
Equal is on the circle.
12. Given the equation of the Circle
(x – 13)2 + (y – 6)2 = 52
Tell if the point is inside or outside the circle.
(5, 6) Outside
(14,8)
13. Given the equation of the Circle
(x – 13)2 + (y – 6)2 = 52
Tell if the point is inside or outside the circle.
(5, 6) Outside
(14,8) In
(20, 9)
14. Given the equation of the Circle
(x – 13)2 + (y – 6)2 = 52
Tell if the point is inside or outside the circle.
(5, 6) Outside
(14,8) In
(20, 9) Outside
15. Given the equation of the Circle
(x – 13)2 + (y – 6)2 = 52
Tell if the point is inside or outside the circle.
(5, 6) Outside
(14,8) In
(20, 9) Outside
(16, 2)
16. Given the equation of the Circle
(x – 13)2 + (y – 6)2 = 52
Tell if the point is inside or outside the circle.
(5, 6) Outside
(14,8) In
(20, 9) Outside
(16, 2) On
