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
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