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Writing and Graphing Equations of Circles

Learn how to write and graph equations of circles, including the standard equation with center and radius. Practice finding the equation of a circle using given coordinates and distance. Includes examples and exercises.

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Writing and Graphing Equations of Circles

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  1. GEOMETRY: Chapter 10 10.6: Write and Graph Equations of Circles

  2. Recall: The equation of a circle with radius r and the center at origin is: x2 + y2 = r2. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 699.

  3. Ex.1: Write the equation of the circle shown. Answer: x2 + y2 = 16 Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 7001.

  4. Standard Equation of a Circle The standard equation of a circle with center (h, k) and radius r is: (x – h)2 + (y – k)2 = r2

  5. Ex. 2: Write the standard equation of a circle with center (-2, 3) and radius 3.8. Answer: (x + 2)2 + (y – 3)2 = 14.44

  6. Ex. 3: The point (8, -1) is on a circle with center (4, 2). Write the standard equation of the circle. Answer: (x – 4)2 + (y – 2)2 = 25

  7. Ex. 4: The equation of a circle is (x + 1)2 + (y – 3)2 = 4. Graph the circle.

  8. Ex. 4: The equation of a circle is (x + 1)2 + (y – 3)2 = 4. Graph the circle.

  9. Ex. 5: Three forest ranger stations are at A(-3,2), B(2,2), and C(-1, -1.5). A fire is 2 miles from A, 3 miles from B, and 3.5 miles from C. Find the location of the fire by graphing.

  10. Ex. 5: Three forest ranger stations are at A(-3,2), B(2,2), and C(-1, -1.5). A fire is 2 miles from A, 3 miles from B, and 3.5 miles from C. Find the location of the fire by graphing.

  11. 10.6, p. 638, #3-31 odds, (15 questions)

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