1. Objective: To write an equation of a circle.
11.5 Equations of Circles
Objective: To write an equation of a circle.

2. Equation of a Circle The center of a circle is given by (h, k)
The radius of a circle is given by r
The equation of a circle in standard form is
(x – h)2 + (y – k)2 = r2

3. Ex. 1: Writing a Standard Equation of a Circle
Write the standard equation of the circle with a center at (-4, 0) and radius 7.1
(x – h)2 + (y – k)2 = r2
Standard equation of a circle.
Substitute values.
[(x – (-4)]2 + (y – 0)2 = 7.12
Simplify.
(x + 4)2 + (y – 0)2 = 50.41

4. Example 2:Writing Equations of Circles
Write the standard equation of the circle: Center (-3, 8) Radius of 6.2 (x + 3)2 + (y – 8)2 = 38.44
(x – h)2 + (y – k)2 = r2
[(x – (-3)]2 + (y – 8)2 = 6.22

5. Example 3: Writing Equations of Circles
Write the standard equation of the circle: Center (0, 6) Radius of x 2 + (y – 6)2 = 7
(x – h)2 + (y – k)2 = r2
[(x – 0]2 + (y – 6)2 = (√7)2

6. Example 4: Writing Equations of Circles
Write the standard equation of the circle: Center (-1.9, 8.7) Radius of 3 (x + 1.9)2 + (y – 8.7)2 = 9
(x – h)2 + (y – k)2 = r2
[(x – (-1.9)]2 + (y – 8.7)2 = 32

7. Ex. 5: Writing a Standard Equation of a Circle
The point (1, 2) is on a circle whose center is (5, -1). Write a standard equation of the circle.
r =
Use the Distance Formula
r =
Substitute values.
r =
Simplify.
r =
Simplify.
r =
Addition Property
Square root the result.
r = 5

8. Ex. 5 (cont.): Writing a Standard Equation of a Circle
The point (1, 2) is on a circle whose center is (5, -1). Write a standard equation of the circle.
(x – h)2 + (y – k)2 = r2
Standard equation of a circle.
Substitute values.
[(x – 5)]2 + [y –(-1)]2 = 52
Simplify.
(x - 5)2 + (y + 1)2 = 25

9. Ex. 6: Writing a Standard Equation of a Circle
The point (-1,-4) is on a circle whose center is (-4, 0). Write a standard equation of the circle.
r =
Use the Distance Formula
Substitute values.
r =
r =
Simplify.
r =
Simplify.
r =
Addition Property
Square root the result.
r = 5

10. Ex. 6 (cont.): Writing a Standard Equation of a Circle
The point (-1, -4) is on a circle whose center is (-4, 0). Write a standard equation of the circle.
(x – h)2 + (y – k)2 = r2
Standard equation of a circle.
Substitute values.
[(x – (-1))]2 + [y –(-4)]2 = 52
Simplify.
(x - 1)2 + (y + 4)2 = 25

11. Example 7: Give the center and radius of the following circles: A.B.
Center: ( 4, 3 ) ; Radius: 4
Center: ( 0, -7 ) ; Radius: 1

12. Assignment
Page 617
#1 - 15