1. Equations of Circles

2. Equation of a Circle
Standard Equation of a Circle: An equation of a circle with center (h, k) and radius r is (x – h)2 + (y – k)2 = r2.

3. Finding the Center and the Radius when given the equation
Center (0, 0), r = 5
Center (0, 0), r = 10
Center (5, -4), r = 7
Center (-7, 3), r =
Center (0, 1), r =
Center (3, 0), r = 9

4. Writing the Equation of a Circle
Center (0, 0) r = 2
Center (0, 1) r = 6
Center (-3, 5) r = 2.5
Center (-5, 10) r = 10
Center (8, 0) r = 1
Center (6, 9) r = 3.4
x2 + y2 = 4
x2 + (y – 1)2 = 36
(x + 3)2 + (y– 5)2= 6.25
(x + 5)2 + (y–10)2= 100
(x – 8)2 + y2= 1
(x– 6)2 + (y– 9)2= 11.56

5. Writing the Equation of a circle
2. A circle whose center is at (-3, 2) passes through (-7, 2).
What is the length of the radius of the circle?
Write the equation
of the circle.
Answers:
a. r = 4
b. (x + 3)2 + (y - 2)2 = 16

6. Graphing a Circle Find the center and the radius and graph the circle.
Answers:
center (0, 0)
radius = 3

7. Graphing a Circle Find the center and the radius and graph the circle.
Answers:
center (1, -2)
radius = 5

8. Graphing a Circle Find the center and the radius and graph the circle.
Answers:
center (3, 0)
radius = 2

9. Graphing a Circle Given Its Equation
Graph the circle whose equation is (x + 4)2 + (y – 1)2 = 25.

10. Converting from General Form to Standard
Move the x terms together and the y terms together.
Move C to the other side.
Complete the square (as needed) for x.
Complete the square(as needed) for y.
Factor the left & simplify the right.

11. WRITE and GRAPH A) write the equation of the circle in standard form
x² + y² - 4x + 8y + 11 = 0
Group the x and y terms
x² - 4x + y² + 8y + 11 = 0
Complete the square for x/y
x² - 4x y² + 8y + 16 =
(x – 2)² + (y + 4)² = 9
YAY! Standard Form!
B) GRAPH
Plot Center (2,-4)
Radius = 3

12. WRITE and GRAPH A) write the equation of the circle in standard form
4x² + 4y² + 36y + 5 = 0
Group the x and y terms
Complete the square for x/y
4x² + 4(y² + 9y) = -5
4x² + 4(y² + 9y + 81/4) =
4x² + 4(y + 9/2)² = 76
x² + (y + 9/2)² = 19
YAY! Standard Form!
B) GRAPH
Plot Center (0 , -9/2)
Radius = √19 = 4.5

13. 8. Write the standard equation of the circle. State the center & radius.

14. 9. Write the standard equation of the circle. State the center & radius.

15. 10. Write the standard equation of the circle
10. Write the standard equation of the circle. State the center & radius.

16. Example: Write the equation and find the center and radius length of :
Group terms
Complete the square

17. Write the equation and find the center and radius length of :