Circles

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