1. 8.3: Circles Write equations of circles Graph circles

2. Circle A circle is the set of all point in a plane that are equidistant from a given point in the plane, called the center. Equation of a circle: (x – h) 2 + (y – k) 2 = r 2

3. Example One: Write an equation for the circle that satisfies each set of conditions: Center (8, -3), Radius 6 Center (5, -6), Radius 4

4. Example One: Write an equation for the circle that satisfies each set of conditions: Center (-5, 2) passes through (-9, 6) Center (7, 7) passes through (12, 9)

5. Example One: Write an equation for the circle that satisfies each set of conditions: Endpoints of a diameter are (-4, -2) and (8, 4) Endpoints of a diameter are (-4, 3) and (6, -8)

6. Graph circles Make sure the equation is in standard form Graph the center Use the length of the radius to graph four points on the circle (up, down, left, right) Connect the dots to create the circle

7. Example Two: Find the center and radius of the circle given the equation. Then graph the circle (x – 3) 2 + y 2 = 9

8. Example Two: Find the center and radius of the circle given the equation. Then graph the circle (x – 1) 2 + (y + 3) 2 = 25

9. Example Two: Find the center and radius of the circle given the equation. Then graph the circle x 2 + y 2 – 10x + 8y + 16 = 0

10. Example Two: Find the center and radius of the circle given the equation. Then graph the circle x 2 + y 2 – 4x + 6y = 12

11. Classwork/Homework Workbook Lesson 8.3 1 – 13 (all)

12. Homework Answers: Workbook 8.3 1.(x + 4) 2 + (y – 2) 2 = 64 2.x 2 + y 2 = 16 3.(x + ¼) 2 + (y + ) 2 = 50 4.(x – 2.5) 2 + (y – 4.2) 2 = 0.81 5.(x + 1) 2 + (y + 7) 2 = 5 6.(x + 9) 2 + (y + 12) 2 = 74 7.(x + 6) 2 + (y – 5) 2 = 25 8.(-3, 0); r = 4 9.(0, 0); r = 2 10.(-1, -3); r = 6 11.(1, -2); r = 4 12.(3, 0); r = 3 13.(-1, -3); r = 3