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Circles in the Coordinate Plane

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

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Circles in the Coordinate Plane

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  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. GEOMETRY LESSON 11-5 Circles in the Coordinate Plane (x – h)2 + (y – k)2 = r2Standard form (x + 8)2 + y2 = 5 Simplify.

  2. Write the standard equation of a circle with center (5, 8) that passes through the point (–15, –13). 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 GEOMETRY LESSON 11-5 Circles in the Coordinate Plane First find the radius. Then find the standard equation of the circle with center (5, 8) and radius 29.

  3. (continued) Then find the standard equation of the circle with center (5, 8) and radius 29. GEOMETRY LESSON 11-5 Circles in the Coordinate Plane (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.

  4. 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 = 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. GEOMETRY LESSON 11-5 Circles in the Coordinate Plane

  5. 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. GEOMETRY LESSON 11-5 Circles in the Coordinate Plane 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.

  6. (1, –1); r = 3 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) (x – 10)2 + (y – 35)2 = 625 x2 + (y + 6)2 = 11 (x – 3)2 + (y – 2)2 = 81 (x + 9)2 + (y – 5)2 = 20

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