9) equations of circles

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Equations of Circles
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Definitions

• Circle The set of all points that are the same
  distance from a center point
• Radius a segment whose endpoints are the center
  and a point on the circle

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Diameter A segment that goes through the
center and end points are points on the circle.
The diameter cuts the circle in half And is twice
the length of the radius
diameter
radius
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Equation of a Circle
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No matter where the circle is located, or where
the center is, the form of the equation is the
same.
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Graph the circle. identify the center radius.
(x 3)2 (y 2)2 9 Center (3, 2) Radius
of 3
Plot the center point and then use the radius to
find other points. Then connect.
7
Graph the circle. identify the center radius.
x 2 (y 3)2 16 Center (0, -3) Radius of 4
Plot the center point and then use the radius to
find other points. Then connect.
8
Graph the circle. identify the center radius.
(x 3) 2 (y 1)2 4 Center (-3, 1) Radius
of 2
Plot the center point and then use the radius to
find other points. Then connect.
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Write an equation of a circle with center
(3 , -2) and a radius of 4.
h
k
r
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Find the center, radius, equation of the circle.
(0, 0)
The center is The radius is The equation is
12
x2 y2 144
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EX 2 Write an equation of a circle with center
(-4, 0) and a diameter of 10.
h
k
r
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EX 3 Write an equation of a circle with center
(2, -9) and a radius of .
h
k
r
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Writing the Equation of a Circle

• Group x terms together, y-terms together, and
  move constants to the other side
• Complete the square for the x-terms
• Remember that whatever you do to one side, you
  must also do to the other
• Complete the square for the y-terms
• Remember that whatever you do to one side, you
  must also do to the other

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Example Write the equation and find the center
and radius length
Group terms
Complete the square
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Write the equation and find the center and radius
length of
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Write the standard equation of the circle. State
the center radius.
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Write the general form of the equation of the
circle.