Conic Sections

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Conic Sections

• Circles

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Conic Sections CirclesThe coefficients of x2
and y2

• The coefficients of x2 and y2 have the same sign
  and same value.
• An example of this is
• x2 y2 25
• It is easy to see that the coefficients for x2
  and y2 are both equal to positive 1.

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Conic Sections CirclesCoordinate Values of
(h,k)

• The point (h,k) represents the center of the
  circle.
• In the example x2 y2 25, the center is at
• (h,k) (0,0)

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Conic Sections - CirclesThe radius of the circle

• In the example x2 y2 25 the length of the
  radius is the square root of 25.
• The radius of this circle has a value,
• r 5

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Conic Sections CirclesExample 1 - Graph it!

• The quadratic relationship being graphed is x2
  y2 25
• The coefficients of x2 and y2 are both equal to
  positive one. This tells us this conic section
  is a CIRCLE.
• Center (h,k) (0,0)
• Radius 5

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Conic Sections CirclesExample 2 - Graph it!

• The quadratic relationship being graphed is
  (x-2)2 (y1)2 25
• The coefficients of x2 and y2 are both equal to
  positive one. This tells us this conic section
  is a CIRCLE.
• Center (h,k) (2,-1)
• Radius 5

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