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 = r 2

7. Examples Ex: x 2 + y 2 = 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  x 2 + 2x + 1 + y 2 = 4  x 2 + y 2 – 4y – 16 = 0  x 2 – 4x + 5 + y 2 + 2y = 25

10. Graphing Circles  x 2 + y 2 = 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 x 2 + y 2 = 9 four units left and three units up.  For the translation of x 2 + y 2 = 1 five units left and three units down.  For the translation of x 2 + y 2 = 4 two units right and seven units up.

16. Homework!  Worksheet