11.5 Equations of Circles

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11.5 Equations of Circles

• Objective To write an equation of a circle.

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Graphing Circles

• If you know the equation of a circle, you can
  graph the circle by identifying its center and
  radius.

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Ex. 1 Graphing a circle

• The equation of a circle is
• (x2)2 (y-3)2 9. Graph the circle.
• First rewrite the equation to find the center and
  its radius.

• (x2)2 (y-3)2 9
• x (-2)2 (y 3)232
• The center is (-2, 3) and the radius is 3.

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Ex. 1 (cont.) Graphing a circle

• To graph the circle, place a point at (-2,
  3), set the radius at 3 units.

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Example 2Finding the Equation of a Circle
Circle A The center is (16, 10) The radius
is 10 The equation is (x 16)2 (y 10)2
100
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Example 3 Finding the Equation of a Circle

• Circle B
• The center is (4, 20)
• The radius is 10
• The equation is
• (x 4)2 (y 20)2 100

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Example 4 Finding the Equation of a Circle
Circle O The center is (0, 0) The radius is
12 The equation is x 2 y 2 144
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Example 5 Graphing Circles
(x 3)2 (y 2)2 9 Center (3, 2) Radius
of 3
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Example 6 Graphing Circles
(x 4)2 (y 1)2 25 Center (-4, 1) Radius
of 5
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Assignment

• Page 617
• 16-23