Title: 11.5 Equations of Circles
111.5 Equations of Circles
- Objective To write an equation of a circle.
2Graphing Circles
- If you know the equation of a circle, you can
graph the circle by identifying its center and
radius.
3Ex. 1 Graphing a circle
- The equation of a circle is
- (x2)2 (y-3)2 9. Graph the circle.
- First rewrite the equation to find the center and
its radius.
- (x2)2 (y-3)2 9
- x (-2)2 (y 3)232
- The center is (-2, 3) and the radius is 3.
4Ex. 1 (cont.) Graphing a circle
- To graph the circle, place a point at (-2,
3), set the radius at 3 units.
5Example 2Finding 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
6Example 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
7Example 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
8Example 5 Graphing Circles
(x 3)2 (y 2)2 9 Center (3, 2) Radius
of 3
9Example 6 Graphing Circles
(x 4)2 (y 1)2 25 Center (-4, 1) Radius
of 5
10Assignment