1. 4 minutes
Warm-Up
1. Graph the equation x2 - 8x – y + 20 = 0. Label the vertex, focus, and directrix.

2. 9.3.1 Circles
Objectives:
Write an equation for a circle given sufficient information
Given an equation of a circle, graph it and label the radius and the center

3. Standard Equation of a Circle
OP = r
P(x,y) r O

4. Standard Equation of a Circle
An equation for the circle with its center at (0,0) and a radius of r is

5. Example 1
Write the standard equation of the circle whose center is at the origin and whose radius is 4. Sketch the graph. -4 -2 2 4

6. Standard Equation of a Circle
The standard equation for a translated circle is
(x – h)2 + (y – k)2 = r2
center: (h, k)
radius: r

7. Example 2 Write the standard equation of the circle graphed below. -6-8 6 8 2 4 -4 -2

8. Practice
Write the standard equation of a circle with the following center and radius.
1) C(0,0) radius: 9
2) C(2,3) radius: 5
3) C(-5,2) radius: 4

9. Practice Graph each equation. Label the center and radius.
1) x2 + y2 = 25
2) (x – 2)2 + y2 = 4
3) (x + 4)2 + (y – 3)2 = 49

10. Homework
p.583 #11-21 odds; odds

11. 4 minutes
Warm-Up
1. Graph the equation x2 + (y + 3)2 = 16. Label the center and the radius.

12. 9.3.2 Circles
Objectives:
Write an equation for a circle given sufficient information
Given an equation of a circle, graph it and label the radius and the center

13. Example 1
Write the standard equation for the circle given by x2 + y2 – 12x – 2y - 8 = 0. State the coordinates of its center and give its radius.
Center:
(6,1)
Radius:

14. Example 2
Write the standard equation for the circle given by x2 + y2 + 6x – 4y - 3 = 0. State the coordinates of its center and give its radius. Then sketch the graph. -6 -8 6 8 2 4 -4 -2
Center:
(-3,2)
Radius:

15. Practice
Write the standard equation for the circle given by x2 + y2 - 2x + 2y - 7 = 0. State the coordinates of its center and give its radius. Then sketch the graph.

16. Homework
p.583 #25,27,41,43,49,51,55