1. Standard Equation of a Circle Definition of a Circle
10.6 Equations of a Circle
Standard Equation of a Circle
Definition of a Circle

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)

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

5. Equations we’ll need:
Distance formula
Midpoint formula

6. Example 4 radius radius C
Find the radius, graph the circle, and write the equation in standard form with the given center of (2, -3) and the point (1, 0).
radius
radius C
2.3 - Circles
4/15/ :07 AM 6 6

7. Example 4
Find the radius, graph the circle, and write the equation in standard form with the given center of (2, -3) and the point (1, 0).
radius = C
2.3 - Circles
4/15/ :07 AM 7 7

8. Write the equation of Circle
Center at ( -5,0) and radius 4.8
h =?
k =?
r = 4.8

9. Write the equation of Circle
Center at ( -5,0) and radius 4.8
h =-5
k =0
r = 4.8

10. Write the equation of Circle
Center at ( 4, -3) and
a point on the circle (2,1)
h =
k =
r =
x =
y =

11. 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

12. 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

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)

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) (5 -13)2 + (6 – 6)2 is it <, >, or = 52
( - 8) = = 25
Greater then outside the circle.
Less then Inside the circle.
Equal is on the circle.

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)

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)

17. 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

18. 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)

19. 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

20. Homework
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