Name
Class
Date
Reteaching 10-3
OBJECTIVE: Finding the center and radius of
a circle
Circles
MATERIALS: None
• When working with circles, begin by writing the equation in
standard form:
(x - h)2 + (y - k)2 = r2
Find the radius and center of the circle with equation (x - 2)2 + (x + 3)2 = 16.
(x - 2)2 + (y + 3)2 = 16
The given equation is in standard form.
(x - 2)2 + (y - (-3))2 = 16
Because standard form has (y – k), change the
addition to subtraction.
h = 2, k = -3
Find h and k.
(2, -3)
The center is (h, k).
r2 = 16
Find r.
r=4
Take the square root of each side. Since radius is a
distance, ignore the negative value.
The center is (2, -3) and the radius is 4.
Exercises
Find the radius and center of each circle.
1. (x - 5)2 + (y - 2)2 = 9
2. (x + 8)2 + (y - 4)2 = 8
3. (x - 4)2 + (y + 3)2 = 20
4. (x - 3)2 + y2 = 6
5. x2 + (y - 5)2 = 25
6. (x + 6)2 + (y + 7)2 = 1
7. (x + 1)2 + (y + 2)2 = 36
8. (x - 2)2 + (y - 5)2 = 4
9. x2 + y2 = 4
10. (x - 1)2 + (y + 3)2 = 9
11. (x - 2)2 + (y - 3)2 = 12
12. (x + 1)2 + (y - 3)2 = 25
13. x2 + (y + 3)2 = 45
14. (x + 4)2 + y2 = 63
15. (x + 2)2 + (y - 6)2 = 75
16. (x - 7)2 + (y + 3)2 = 18
17. (x - 4)2 + (y + 1)2 = 24
18. (x + 9)2 + (y - 9)2 = 81
10
Lesson 10-3 Reteaching
Algebra 2 Chapter 10
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Example
All rights reserved.
• Unlike equations of parabolas, which include either x2 or y2, the
equation of a circle will include both x2 and y2.