1. Warm-up: Check the equation for symmetry. y = x3 + 2
HW: WRITING EQUATIONS FOR CIRCLES

2. HW answers: pg (2, 6, 9, 11, 14, 16, 22, 24, 30, 32, matching, symmetry only: even 40-52)
2) a. yes b. No
6) a. no b. yes 9)
11)
Intercepts: (-1, 0), (3, 0), (0, -3)
16) Intercepts: (3, 0), (-3, 0), (0, 9)

3. 22) x-axis symmetry 24) y-axis symmetry 30) 32) 33) C 34) A 35) F
HW answers: pg (2, 6, 9, 11, 14, 16, 22, 24, 30, 32, matching, symmetry only: even 40-52)
22) x-axis symmetry
24) y-axis symmetry
30)
32)
33) C
34) A
35) F
36) E
37) B
38) D
No symmetry
42) y-axis symmetry
44) No symmetry
46) No symmetry
48) No symmetry
50) y-axis symmetry
52) x-axis Symmetry

4. Objectives: Find the center and radius of a circle given its equation.
Write the equation of a circle given its center and a solution point.
Write the equation of a circle given two solution points on its diameter.
Graph a circle given its equation.

5. Circle
The set of all coplanar points is a circle if and only if they are equidistant from a given point in the plane.

6. Standard Equation of a Circle
Find the equation of points (x, y) that are r units from (h, k).

7. Standard Equation of a Circle
Standard form of the equation of a circle:
(h, k) = center point
r = radius

8. Example 1
Find the center and radius of the circle, and then sketch the graph.
(h, k) = center point, r = radius
(-2, 3) = center point, 2 = radius

9. Example 2
The point (1, -2) lies on the circle whose center is at (-3, -5). Write the standard form of the equation of the circle.
(h, k) = center point, r = radius
(1, -2)
(-3, -5)

10. Example 3:
Write the equation in standard form with the given center of (2, -3) and the solution point (1, 0).
radius
radius C 10

11. Example 4:
Write a circle equation whose endpoints of a diameter are (-5, 2) and (3, 6).
Diameter
Center 11

12. Example 4 cont.
Write a circle equation whose endpoints of a diameter are (-5, 2) and (3, 6).
Center
Radius
Radius 12

13. Example 4 cont.
Write a circle equation whose endpoints of a diameter are (-5, 2) and (3, 6). 13

14. x2 + 4x + y2 – 6y = 3 +4 +9 +4 +9 (x + 2)2 + (y – 3)2 = 16 C (-2, 3)
Example 5:
Find the center and radius of the circle with equation x2 + y2 + 4x – 6y – 3 = 0, then graph.
x2 + 4x y2 – 6y = 3 +4 +9 +4 +9
(x + 2) (y – 3)2 = 16
C (-2, 3)
r = 4

15. Summary: Find the center and radius of a circle given its equation.
Write the equation of a circle given its center and a solution point.
Write the equation of a circle given two solution points on its diameter.
Graph a circle given its equation.

16. Sneedlegrit:
The point (1, 2) lies on the circle with center at (-2, -3). Write the standard form of the equation of the circle.
HW: WRITING EQUATIONS FOR CIRCLES