CIRCLES

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CIRCLES

• Topic 10.2

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Definitions

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

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Equation of a Circle
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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 of
Group terms
Complete the square
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You try!! Write the equation and find the center
and radius length of
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THINK ABOUT IT
Find the center, the length of the radius, and
write the equation of the circle if the endpoints
of a diameter are (-8,2) and (2,0).
Center Use midpoint formula!
Length use distance formula with radius and an
endpoint
Equation Put it all together
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THINK ABOUT IT

• Write the equation of a circle whose center is
  (2, -1) and tangent to x 6

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THINK ABOUT IT

• Write the equation of a circle who passes through
  (-2, 3) and is centered at (2, -1)