This document provides instruction on graphing and writing equations for circles. It begins by listing the components needed to graph a circle: the center (h, k) and radius r. Standard circle equation is given as (x - h)2 + (y - k)2 = r2. Several worked examples are shown of identifying center and radius from equations and graphing circles. Students are then asked to graph additional circles on their own and write equations for circles given center and radius. The document concludes by assigning a worksheet as homework.

1. Warm-up

3. What do we need to keep the same?

4. What do we need to change?

5. Chapter 8
Conic Sections
“Circles”

6. What do you need to graph a circle?
 Center (h, k)
 Radius = r
 Standard form of a circle:
 (x - h)2
+ (y - k)2
= r2

7. Examples
 Ex: x2
+ y2
= 25
 Center (0, 0) Radius = 5
 Ex: (x-2)2
+ (y+4)2
= 49
 Center (2, -4) Radius = 7

8. State the center and the radius for each:
 (x + 4)2
+ (y - 6)2
= 36
 (x + 1)2
+ (y - 3)2
= 49
 (x + 3)2
+ (y + 90)2
= 50
 (x + 37)2
+ (y - 12)2
= 50

9. State the center and the radius
 x2
+ 2x + 1 + y2
= 4
 x2
+ y2
– 4y – 16 = 0
 x2
– 4x + 5 + y2
+ 2y = 25

10. Graphing Circles
 x2
+ y2
= 25
 (x-2)2
+ (y+4)2
= 49

11. Now you graph these on your own!
 (x - 3)2
+ (y - 1)2
= 9  (x - 5)2
+ (y - 4)2
= 16

12. Graph on your own…
 (x - 1)2
+ (y - 5)2
= 25  (x + 2)2
+ (y - 7)2
= 36

13. Keep going!
 (x + 7)2
+ (y + 5)2
= 49  (x + 8)2
+ (y + 10)2
= 50

14. Write the equation of the circle
 Center (-4, 3) radius = 4
 Center (5, -2) radius = 8
 Center (-2, 3) radius = 3

15. Write the equation of the circle
 For the translation of x2
+ y2
= 9 four units left and three units up.
 For the translation of x2
+ y2
= 1 five units left and three units down.
 For the translation of x2
+ y2
= 4 two units right and seven units up.

16. Homework!
 Worksheet