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CCGPS GEOMETRY UNIT QUESTION: How are the equations of circles and parabolas derived? Standard: MCC9-12..A.REI.7, G.GPE.1,2 and 4 Today’s Question: How is the equation of a circle derived? Standard: MCC9-12..G.GPE.1 UNIT QUESTION: How are the equations of circles and parabolas derived? Standard: MCC9-12..A.REI.7, G.GPE.1,2 and 4 Today’s Question: How is the equation of a circle derived? Standard: MCC9-12..G.GPE.1

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EOCT PRACTICE QUESTION

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What are the coordinates of this circle’s center? What is its radius?

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EQUATIONS OF CIRCLES

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Standard Form of a Circle Circle with center at the origin (0,0) Standard form of a circle that is translated **Center: (h, k) Radius: r **

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FINDING THE EQUATION OF A CIRCLE Write the standard form of the equation for the circle that has a center at the origin and has the given radius. 1.r = 92.r = 143.

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WRITING EQUATIONS OF CIRCLES Write the standard equation of the circle: Center (4, 7) Radius of 5 (x – 4) 2 + (y – 7) 2 = 25

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Write the standard equation of the circle: Center (-3, 8) Radius of 6.2 (x + 3) 2 + (y – 8) 2 = 38.44 Writing Equations of Circles

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WRITING EQUATIONS OF CIRCLES Write the standard equation of the circle: Center (2, -9) Radius of (x – 2) 2 + (y + 9) 2 = 11

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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 = r 2

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GRAPHING CIRCLES (x – 3) 2 + (y – 2) 2 = 9 Center (3, 2) Radius of 3

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GRAPHING CIRCLES (x + 4) 2 + (y – 1) 2 = 25 Center (-4, 1) Radius of 5

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GRAPHING CIRCLES (x – 5) 2 + y 2 = 36 Center (5, 0) Radius of 6

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Graphing a circle in Standard Form!! Example: Center: (4, 0) r: 3 To write the standard equation of a translated circle, you may need to complete the square. To write the standard equation of a translated circle, you may need to complete the square. Standard Form!!

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WRITE THE STANDARD EQUATION FOR THE CIRCLE. STATE THE CENTER AND RADIUS.

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Write the standard equation for the circle. State the center and radius.

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