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

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

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

4. 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

5. 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

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

7. 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

8. Practice Graph each equation. Label the center and radius.
1) x2 + y2 = 25
Center = (0, 0) radius = 5
2) (x – 2)2 + y2 = 4
Center = (2, 0) radius = 2
3) (x + 4)2 + (y – 3)2 = 49
Center = (-4, 3) radius = 7

9. Example 3
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:

10. Example 4
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:

11. 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.
Center = (1, 1)
Radius = 3