The document discusses the standard equation of a circle. It explains that if the circle is centered at the origin (0,0), the equation is x2 + y2 = r2, where r is the radius. If the circle is not centered at the origin, the equation is (x - h)2 + (y - k)2 = r2, where (h, k) are the coordinates of the center and r is the radius. The document provides examples of writing the equation of a circle given the center and radius. It also demonstrates how to determine if a point lies inside, outside, or on the circle given the equation.

2. Standard equation of the circle
If the circle is at the origin
x 2 + y 2 = r 2 r is the radius
If the circle is not at the origin
The center is at (h, k)
    2
2
2
r
k
y
h
x 




3. Standard equation of the circle
If the circle is at the origin
x 2 + y 2 = r 2 r is the radius
If the circle is not at the origin
Solve for r
    2
2
2
r
k
y
h
x 



   2
2
k
y
h
x
r 




4. General Form of the Equation of a Circle
+ = 9
+ 4 + 9 – 9 = 0

5. + = 25
+ 1 + 16 – 25= 0

6.     2
2
2
r
k
y
h
x 



Ex.
+ = 76 + 4 +1

7.     2
2
2
r
k
y
h
x 



Ex.
+ = -2 + 9 +9

8.     2
2
2
r
k
y
h
x 



(h,k) - center
r- radius
center
(0,0)
Radius(12)

9.     2
2
2
r
k
y
h
x 



(h,k) - center
r- radius
center
(-2,1)
radius

10. center
(1,0)
radius (3)

11. Center (h,k)______
Radius_____
h = 2 k = -3 r = 3
(2,3)

12. = 2
= -3
Center(2,-3)
Radius(3)

13. Center:(-2,1)
Radius: 9

14. Write the equation of Circle
Center at ( 2, -5) and radius is 3
h = 2
k = - 5
r = 3
    2
2
2
r
k
y
h
x 




15. Write the equation of Circle
    2
2
2
r
k
y
h
x 



+ = 10

16. Write the equation of Circle
Center at ( 4, -3) and
a point on the circle (2,1)
h = 4
k = - 3
r =
x = 2
y = 1
    2
2
2
r
k
y
h
x 




17. Given the equation of the Circle
(x – 13)2 + (y – 6)2 = 52
Tell if the point is inside or outside the circle.
(5, 6)

18. Given the equation of the Circle
(x – 13)2 + (y – 6)2 = 52
Tell if the point is inside or outside the circle.
(5, 6) (5 -13)2 + (6 – 6)2 is it <, >, or = 52
( - 8)2 + 02 = 64 = 25
Greater than outside the circle.
Less than Inside the circle.
Equal is on the circle.

19. Given the equation of the Circle
(x – 13)2 + (y – 6)2 = 52
Tell if the point is inside or outside the circle.
(5, 6) Outside
(14,8)

20. Given the equation of the Circle
(x – 13)2 + (y – 6)2 = 52
Tell if the point is inside or outside the circle.
(5, 6) Outside
(14,8) In
(20, 9)

21. Given the equation of the Circle
(x – 13)2 + (y – 6)2 = 52
Tell if the point is inside or outside the circle.
(5, 6) Outside
(14,8) In
(20, 9) Outside

22. Given the equation of the Circle
(x – 13)2 + (y – 6)2 = 52
Tell if the point is inside or outside the circle.
(5, 6) Outside
(14,8) In
(20, 9) Outside
(16, 2)

23. Given the equation of the Circle
(x – 13)2 + (y – 6)2 = 52
Tell if the point is inside or outside the circle.
(5, 6) Outside
(14,8) In
(20, 9) Outside
(16, 2) On

24. Homework
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