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CCGPS Geometry

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. EOCT Practice Question.

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CCGPS Geometry

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  1. 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

  2. EOCT Practice Question • Use the Quadratic formula to find the solutions to the following quadratic equation: • a.) c.) • b.) d.)

  3. Circle: • What are the coordinates of this circle’s center? • What is its radius?

  4. Equations of Circles

  5. 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 **

  6. 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 = 9 2. r = 14 3.

  7. Writing Equations of Circles Write the standard equation of the circle: Center (4, 7) Radius of 5 (x – 4)2 + (y – 7)2 = 25

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

  9. Writing Equations of Circles Write the standard equation of the circle: Center (2, -9) Radius of (x – 2)2 + (y + 9)2 = 11

  10. 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 = r2

  11. Graphing Circles (x – 3)2 + (y – 2)2 = 9 Center (3, 2) Radius of 3

  12. Graphing Circles (x + 4)2 + (y – 1)2 = 25 Center (-4, 1) Radius of 5

  13. Graphing Circles (x – 5)2 + y2 = 36 Center (5, 0) Radius of 6

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

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

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

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