5.2 Graph and Write Equations of Circles

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5.2 Graph and Write Equations of Circles

• Pg 180

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• A circle is an infinite set of points in a plane
  that are equal distance away from a given fixed
  point called a center.
• A radius is a segment that connects the center
  and one of the points on the circle.
• Every radius is equal in length. (radii)
• A diameter is a line segment that connects two
  points on the circle and goes through the center.

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• The formula for a circle with its center at (0,0)
  and a radius of r is
• Example What is the equation for a circle whose
  center is at (0,0) and has a radius of 6.
• Answer ?

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• Example 2 Identify the center and the radius
  of the following
• Answer ?
• Center
• (0,0)
• Radius
• 10

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• Write an equation for the following in standard
  form.

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Graph the Equation of a Circle

• Graph x2 25 y2

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Write an Equation of a Circle

• The point (6, 2) lies on a circle whose center is
  the origin. Write the standard form of the
  equation of the circle.
• We need to find the radius.
• Use the distance formula.

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• If a circle has a translated center then the new
  equation will be
• Where the new center will be (h, k) and r will
  be the radius.

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• Example 1. Write the standard equation for a
  circle whose center is at (-3,5) and has a radius
  of 7.
• Answer Since h-3 and k5 and r7 we can
  substitute these into the equation
• Therefore
• Or

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• Example 2 Given the following equation, identify
  the center and the radius.
• Center ?
• Did you say (7,-2)
• Radius ?
• I bet you said (drum roll please)
• 9
• You guys are AWESOME !!!

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• Example 3 Given the following graph answer the
  following questions.
• 1. Identify the center.
• 2. Name the radius.
• 3. Write an equation in standard form for the
  circle.

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(No Transcript)
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Answers

• Center (-2,-1)
• Radius 8
• Equation

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Finding the equation of a Tangent Line to a
Circle

• Any line tangent to a circle will be
  perpendicular to a line that goes through the
  tangent point and the center of the circle
• Perpendicular lines have negative reciprocal
  slopes
• (Opposite Reciprocal)
• So if we have the center of a circle, and the
  point of tangency, we can find the slope by the
  slope formula
• Take the negative reciprocal and use the point
  slope formula for a line that goes through the
  tangent point

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Find the equation of a Tangent Line to a circle

• Find the equation of a tangent line to the circle
  x2 y2 10 at (-1, 3)

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Assignment

• Pg 182
• 1 23, 24 odd