[x – (–8)] 2 + (y – 0) 2 = ( 5 ) 2 Substitute (–8, 0) for (h, k) and 5 for r. Write the standard equation of a circle with center (–8, 0) and radius 5. (x – h) 2 + (y – k) 2 = r 2 Standard form (x + 8) 2 + y 2 = 5Simplify. GEOMETRY LESSON 11-5 Circles in the Coordinate Plane

r = (x – h) 2 + (y – k) 2 Use the Distance Formula to find r. = (–15 – 5) 2 + (–13 – 8) 2 Substitute (5, 8) for (h, k) and (–15, –13) for (x, y). Write the standard equation of a circle with center (5, 8) that passes through the point (–15, –13). First find the radius. = (–20) 2 + (–21) 2 Simplify. = = 841 = 29 Then find the standard equation of the circle with center (5, 8) and radius 29. GEOMETRY LESSON 11-5 Circles in the Coordinate Plane

Then find the standard equation of the circle with center (5, 8) and radius 29. (continued) (x – h) 2 + (y – k) 2 = r 2 Standard form (x – 5) 2 + (y – 8) 2 = 29 2 Substitute (5, 8) for (h, k) and 29 for r. (x – 5) 2 + (y – 8) 2 = 841Simplify. GEOMETRY LESSON 11-5 Circles in the Coordinate Plane

Find the center and radius of the circle with equation (x + 4) 2 + (y – 1) 2 = 25. Then graph the circle. (x + 4) 2 + (y – 1) 2 = 25 (x – (– 4)) 2 + (y – 1) 2 = 5 2 Relate the equation to the standard form (x – h) 2 + (y – k) 2 = r 2. h k r The center is (– 4, 1) and the radius is 5. GEOMETRY LESSON 11-5 Circles in the Coordinate Plane

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 = r 2 Use standard form. (x – 6) 2 + [y – (–12)] 2 = 80 2 Substitute. (x – 6) 2 + (y + 12) 2 = 6400 This is an equation for the tower. GEOMETRY LESSON 11-5 Circles in the Coordinate Plane

1.Find the center and radius of the circle with equation (x – 1) 2 + (y + 1) 2 = 9. Then graph the circle. 2.A cellular phone tower with a range of 25 units is located on a coordinate grid at (10, 35). Write an equation that describes its position and range. Write the standard equation of each circle. 3.center (0, –6); radius 11 4.center (3, 2); diameter 18 5.center (–9, 5); passing through (–7, 1) (1, –1); r = 3 (x + 9) 2 + (y – 5) 2 = 20 (x – 3) 2 + (y – 2) 2 = 81 x 2 + (y + 6) 2 = 11 (x – 10) 2 + (y – 35) 2 = 625 GEOMETRY LESSON 11-5 Circles in the Coordinate Plane