1. 10.3 Circles 10.3 Circles What is the standard form equation for a circle? Why do you use the distance formula when writing the equation of a circle? What general equation of a circle is used when the center of the circle is translated? How do you put an equation into standard form?

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

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 42 4 -4 -2

5. Standard Equation of a Circle The standard equation for a translated circle is (x – h) 2 + (y – k) 2 = r 2 center: (h, k) radius: r

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

7. Practice 1) C(0,0) radius: 9 Write the standard equation of a circle with the following center and radius. 2) C(2,3) radius: 5 3) C(-5,2) radius: 4

8. Practice 1) x 2 + y 2 = 25 Graph each equation. Label the center and radius. 2) (x – 2) 2 + y 2 = 4 3) (x + 4) 2 + (y – 3) 2 = 49

9. Example 1 Write the standard equation for the circle given by x 2 + y 2 – 12x – 2y - 8 = 0. State the coordinates of its center and give its radius. Center: (6,1) Radius:

10. Example 2 Write the standard equation for the circle given by x 2 + y 2 + 6x – 4y - 3 = 0. State the coordinates of its center and give its radius. Then sketch the graph. Center: (-3,2) Radius: -6 -8 6 8 2 4 -4 -2

11. Practice Write the standard equation for the circle given by x 2 + y 2 - 2x + 2y - 7 = 0. State the coordinates of its center and give its radius. Then sketch the graph.

12. What is the standard form equation for a circle? x 2 + y 2 = r 2 Why do you use the distance formula when writing the equation of a circle? To find the radius of the circle. What general equation of a circle is used when the center of the circle is translated? (x-h) 2 +(y-k) 2 = r 2 How do you put an equation into standard form? Complete the square

13. Assignment 10.3 p.604, 20-25, 26-64 even Skip 36, 44, 46, 56, 58 p. 628, 13, 14, 21, 27