[ x – (– 8 )] 2 + ( y – 0 ) 2 = ( 5 ) 2 Substitute (–8, 0) for ( h , k ) and 5 for r .

1. Write the standard equation of a circle with center (–8, 0) and radius 5. [x – (–8)]2 + (y – 0)2 = ( 5 )2Substitute (–8, 0) for (h, k) and 5 for r. Circles in the Coordinate Plane LESSON 12-5 Additional Examples (x – h)2 + (y – k)2 = r2Standard form (x + 8)2 + y2 = 5 Simplify. Quick Check

2. r = (x – h)2 + (y – k)2Use the Distance Formula to find r. = (–15 – 5)2 + (–13 – 8)2Substitute (5, 8) for (h, k) and (–15, –13) for (x, y). = (–20)2 + (–21)2Simplify. = 400 + 441 = 841 = 29 Circles in the Coordinate Plane LESSON 12-5 Additional Examples Write the standard equation of a circle with center (5, 8) that passes through the point (–15, –13). First find the radius.

3. Circles in the Coordinate Plane LESSON 12-5 Additional Examples (continued) Then find the standard equation of the circle with center (5, 8) and radius 29. (x – h)2 + (y – k)2 = r2Standard form (x – 5)2 + (y – 8)2 = 292Substitute (5, 8) for (h, k) and 29 for r. (x – 5)2 + (y – 8)2 = 841 Simplify. Quick Check

4. (x + 4)2 + (y – 1)2 = 25 (x – (– 4))2 + (y – 1)2 = 52Relate the equation to the standard form (x – h)2 + (y – k)2 = r2. hkr The center is (– 4, 1) and the radius is 5. Circles in the Coordinate Plane LESSON 12-5 Additional Examples Find the center and radius of the circle with equation (x + 4)2 + (y – 1)2 = 25. Then graph the circle. Quick Check

5. Circles in the Coordinate Plane LESSON 12-5 Additional Examples A diagram locates a radio tower at (6, –12) on a coordinate grid where each unit represents 1 mi. The radio signal’s range is 80 mi. Find an equation that describes the position and range of the tower. The center of a circular range is at (6, –12), and the radius is 80. (x – h)2 + (y – k)2 = r2Use standard form. (x – 6)2 + [y – (–12)]2 = 802Substitute. (x – 6)2 + (y + 12)2 = 6400 This is an equation for the tower. Quick Check