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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Equation of a Circle
The center of a circle is given by (h, k) The
radius of a circle is given by r The equation of
a circle in standard form is (x h)2 (y k)2
r2
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Ex. 1 Writing a Standard Equation of a Circle

• Write the standard equation of the circle with a
  center at (-4, 0) and radius 7.1

(x h)2 (y k)2 r2
Standard equation of a circle.
Substitute values.
(x (-4)2 (y 0)2 7.12
Simplify.
(x 4)2 (y 0)2 50.41
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Example 2Writing Equations of Circles

• Write the standard equation of the circle
• Center (-3, 8) Radius of 6.2
• (x 3)2 (y 8)2 38.44

(x h)2 (y k)2 r2
(x (-3)2 (y 8)2 6.22
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Example 3 Writing Equations of Circles

• Write the standard equation of the circle
• Center (0, 6) Radius of
• x 2 (y 6)2 7

(x h)2 (y k)2 r2
(x 02 (y 6)2 (v7)2
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Example 4 Writing Equations of Circles

• Write the standard equation of the circle
• Center (-1.9, 8.7) Radius of 3
• (x 1.9)2 (y 8.7)2 9

(x h)2 (y k)2 r2
(x (-1.9)2 (y 8.7)2 32
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Ex. 5 Writing a Standard Equation of a Circle

• The point (1, 2) is on a circle whose center is
  (5, -1). Write a standard equation of the circle.

Use the Distance Formula
Substitute values.
Simplify.
Simplify.
Addition Property
Square root the result.
r 5
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Ex. 5 (cont.) Writing a Standard Equation of a
Circle

• The point (1, 2) is on a circle whose center is
  (5, -1). Write a standard equation of the circle.

(x h)2 (y k)2 r2
Standard equation of a circle.
Substitute values.
(x 5)2 y (-1)2 52
Simplify.
(x - 5)2 (y 1)2 25
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Ex. 6 Writing a Standard Equation of a Circle

• The point (-1,-4) is on a circle whose center is
  (-4, 0). Write a standard equation of the circle.

Use the Distance Formula
Substitute values.
r
Simplify.
Simplify.
Addition Property
Square root the result.
r 5
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Ex. 6 (cont.) Writing a Standard Equation of a
Circle

• The point (-1, -4) is on a circle whose center is
  (-4, 0). Write a standard equation of the circle.

(x h)2 (y k)2 r2
Standard equation of a circle.
Substitute values.
(x (-1))2 y (-4)2 52
Simplify.
(x - 1)2 (y 4)2 25
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Example 7 Give the center and radius of the
following circles A. B.
Center ( 4, 3 ) Radius 4
Center ( 0, -7 ) Radius 1
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Assignment

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