11-4 Circles in the Coordinate Plane Equation of a Circle Deriving the Equation of a Circle Centered at the Origin Describe the graph of 𝑥 2 + 𝑦 2 =25. The graph is a circle with center at the origin, (0, 0) and radius equal to 5 units.

11-4 Circles in the Coordinate Plane Deriving the Equation of a Circle Centered at (h, k) The equation of a circle is 𝑥 2 + 𝑦 2 =49 . What is the standard form of an equation of the circle after its center is translated left 3 units and up 2 units? 𝒙+𝟑 𝟐 + 𝒚−𝟐 𝟐 =𝟒𝟗 What is the standard equation of each circle? a. center (3, 5); r = 6 b. center (-2, -1); r = 2 𝒙−𝟑 𝟐 + 𝒚−𝟓 𝟐 =𝟑𝟔 𝒙+𝟐 𝟐 + 𝒚+𝟏 𝟐 =𝟐

11-4 Circles in the Coordinate Plane What is the standard equation of the circle with center (4, 3) that passes through the point (-1, 1)? 𝒙−𝟒 𝟐 + 𝒚−𝟑 𝟐 =𝟐𝟗 a. In Problem 5, you found that the center of the circle is (7, -2) and the radius is 8. What does the center of the circle represent? What does the radius represent? HH - page 476 The center of the circle represents the cell tower’s position and the transmission range of a cell tower.

11-4 Circles in the Coordinate Plane b. What is the center and radius of the circle with equation (x - 2)2 + (y - 3)2 = 100? Graph the circle.

11-4 Circles in the Coordinate Plane 1. Your dog is tethered to a doghouse by a 5-m leash. The doghouse is at the point (-2, 3). Which standard equation of a circle describes the boundary of the area your dog can roam? A. (x + 2)2 + (y - 3)2 = 10 B. (x + 2)2 + (y - 3)2 = 25 C. (x - 2)2 + (y + 3)2 = 10 D. (x - 2)2 + (y + 3)2 = 25 2. You place the point of a compass at (-1, 2) and rotate the compass to draw a circle that passes through point (2, -2). Which statement is true about the circle? F. The radius is 25. H. The equation is (x + 1) 2 + (y - 2)2 = 10. G. The diameter is 10. J. The circumference is 25p. 3. Which of the following is the graph of (x - 2)2 + (y + 1)2 = 9? 4. What is the standard equation of a circle with diameter AB with A(5, 4) and B(-1, -4)? F. (x - 5)2 + (y - 4)2 = 10 G. (x + 5)2 + (y + 4)2 = 100 H. (x - 2 2 + y2 = 25 J. (x + 2)2 + y2 = 5