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 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

3. 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 = 92.r = 143.

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. 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

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 = r 2

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

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

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

16. 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!!

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

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