Objective: To write an equation of a circle. 11.5 Equations of Circles Objective: To write an equation of a circle.

Graphing Circles If you know the equation of a circle, you can graph the circle by identifying its center and radius.

Ex. 1: Graphing a circle The equation of a circle is (x+2)2 + (y-3)2 = 9. Graph the circle. First rewrite the equation to find the center and its radius. (x+2)2 + (y-3)2 = 9 [x – (-2)]2 + (y – 3)2=32 The center is (-2, 3) and the radius is 3.

Ex. 1 (cont.): Graphing a circle To graph the circle, place a point at (-2, 3), set the radius at 3 units.

Example 2:Finding the Equation of a Circle Circle A The center is (16, 10) The radius is 10 The equation is (x – 16)2 + (y – 10)2 = 100

Example 3: Finding the Equation of a Circle Circle B The center is (4, 20) The radius is 10 The equation is (x – 4)2 + (y – 20)2 = 100

Example 4: Finding the Equation of a Circle Circle O The center is (0, 0) The radius is 12 The equation is x 2 + y 2 = 144

Example 5: Graphing Circles (x – 3)2 + (y – 2)2 = 9 Center (3, 2) Radius of 3

Example 6: Graphing Circles (x + 4)2 + (y – 1)2 = 25 Center (-4, 1) Radius of 5

Assignment Page 617 #16-23