1. Test Review

2. Question of the Day
EOCT Review

3. UNIT QUESTION: How are the equations of circles and parabolas derived?
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

4. Equations of Circles

5. CONIC SECTIONS
Quadratic Relations
Parabola
Circle
Ellipse
Hyperbola

6. 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 **

7. 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 = r =

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

9. 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

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

11. 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

12. Circle B The center is (4, 20) The radius is 10 The equation is (x – 4)2 + (y – 20)2 = 100

13. Circle O
The center is (0, 0)
The radius is
The equation is
x 2 + y 2 = 144

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

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

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

17. Applying Graphs of Circles
A bank of lights is arranged over a stage. Each light illuminates a circular area on the stage. A coordinate plane is used to arrange the lights, using the corner of the stage as the origin. The equation (x – 13)2 + (y - 4)2 = 16 represents one of the disks of light.
A. Graph the disk of light.
B. Three actors are located as follows: Henry is at (11, 4), Jolene is at (8, 5), and Martin is at (15, 5). Which actors are in the disk of light?

18. Applying Graphs of Circles
Rewrite the equation to find the center and radius.
(x – h)2 + (y – k)2= r2
(x - 13)2 + (y - 4)2 = 16
(x – 13)2 + (y – 4)2= 42
The center is at (13, 4) and the radius is 4. The circle is shown on the next slide.

19. Applying Graphs of Circles
Graph the disk of light
The graph shows that Henry and Martin are both in the disk of light.

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

21. Another one you ask!?! Ok, here it is!!
Write the standard equation for the circle. State the coordinates of its center and give its radius. Then sketch the graph.

22. Last One!!!
Write the standard equation for the circle. State the center and radius.