1. 10-1: The Circle Objectives:
Use the standard and general forms of the equation of a circle
Graph circles
©2002 Roy L. Gover (

2. Applications
The Chunnel
Gears
The Circle:
Wheels

3. Definition
P(x,y)
The circle is the locus (set) of all points that are equidistant from a given point called the center.
Radius
Center
(h,k)

4. Definition
The standard form of the equation of a circle with radius r and center at (h,k) is:

5. Example
Write the equation of the circle with center at (4,-1) and radius of 6 units. Then graph the equation.
Hint: h=4, k=-1 & r2=36

6. Try This
Write the equation of the circle with center at (-5,6) and radius of 5, then graph the equation.

7. Solution
h=-5
k=6
(-5,6)

8. Example
Graph the circle with center at (4,-5) and radius 4 using a graphing calculator ...

9. Steps: 1. Write equation in standard form. 2. Solve for y
3. Enter in calculator: y1 & y2
4. Set window- use Z-Square to make round

10. Try This
Graph the circle with center at (-2,-1) and radius 2 using a graphing calculator ...

11. Solution
h=-2 & k=-1, therefore:
...

12. Solution

13. Example The equation of a circle is:
Find the radius and coordinates of the center.
Hint: Change to standard form by completing the square

14. Try This The equation of a circle is:
Write the equation in standard form. Find the radius and coordinates of the center.

15. Try This The equation of a circle is:
Find the radius and coordinates of the center.
Radius=4; Center: (1,-3)

16. Lesson Close
1. What is h & k ?
2. What is the center & radius of: