1. Equations of Circles

2. Crop Circles
Whether you believe they are fact or faked… they are full of mathematics!!!

3. Introductory Group Activity
Complete the introductory group activity on pages 1 & 2 of your packet

4. Notes: Writing Equations of Circles
Given any point on a circle with center (0,0) the Pythagorean Theorem gives us x2 + y2 = r2 r y x

5. Example
Write the equation for the circle shown in the graph r=
Equation = x2 + y2 = r2= 3 9
x2 + y2 = 9

6. But what if the circle is NOT centered at (0,0)?
Suppose a circle is centered at point (h,k). Use the distance formula to find r.

7. Examples
Write the standard equation for a circle with center (-2,5) and radius 7
(x-h)2 + (y-k)2 = r2
(x- -2)2 + (y- 5)2 = 72
(x+2)2 + (y-5)2 = 49

8. Example
B) The point (-5,6) is on a circle with center (-1,3). Write the equation for the circle.
**Hint: You have to solve for r first! Then write the equation.
(x--1)2 + (y-3)2 = 52
(x-h)2 + (y-k)2 = r2
(-5- -1)2 + (6- 3)2 = r2
(x+1)2 + (y-3)2 = 25
(-4)2 + (3)2 = r2
16+ 9 = r2
25 = r2
5 = r

9. Graphing Circles Example: Graph the circle with the equation
(x-4)2 + (y+2) 2 = 36
Determine center:
Radius is:
Draw point at center; mark radius up, down, left and right and connect freehand or with compass.
(4,-2)
Sqrt(36) = 6

10. Example
(-1,2)

11. Examples Write equations for the circles shown. a) x2 + y2 = 4
b) x2 + y2 = 36
c) (x-2)2 + (y-3)2 = 4

12. Examples
Write the standard equation of the circles with the given center and radii:
A) center: (0,0) radius: 3
B) center: (-2,5) radius: 7
a) x2 + y2 = 36
b) (x+2)2 + (y-5)2 = 49

13. Examples
Write the standard equation of a circle with the given center and point on the circle:
center: (1,4) point (3,4)
center: (2,6) point (-1,2)
center: (-1,2) point (-3,4)
a) (x-1)2 + (y-4)2 = 4
b) (x-2)2 + (y-6)2 = 25
c) (x+1)2 + (y-2)2 = 8

14. Examples
Graph the circles

15. Example
Burial Location:
(-4,8)