1. Lesson 4-1
Circles

2. Standard Form of a Circle
(h,k) is the center of the circle
The radius of the circle is r
When plugging h and k into the equation they will change signs since is subtraction in the standard form of a cirlce

3. Example
Write the equation of a circle with a center at (-3,2) and radius of 4

4. Example
Write the equation of a circle with a center at (1, -4) and a radius of 2

5. You Try
Write the equation of a circle with a center at (4, -11) and a radius of 16

6. Graphing a circle from standard form
Find the center of the circle (h,k) (remember to change signs when pulling them from the equation)
Plot the center of the circle
Find the radius of the circle (square root of r^2 in the equation)
Go left, right, up, and down r units from the center and put a put at each
Draw your best circle through the four points from step 4

7. Example

8. Example

9. You Try

10. Writing an equation from a graph
Find h and k which is the center of the circle
Count from the center of the circle to the outside (this is your radius)
Plug h, k, and r into your standard form for a circle

11. Example

12. Example

13. You Try

14. Finding the center and radius from the standard form equation
Pull out h and k remember to change signs this is your center (h,k)
Find r ( take the square root of the answer)

15. Example
Find the center and the radius of the circle

16. You try
Find the center and radius of the circle

17. Homework
Circle worksheet
Work all the problems