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10.6 Equations of a Circle. Standard Equation of a Circle Definition of a Circle. Definition of a Circle. A circle is a set of points a given distance from one point called the center. The distance from the center is called the radius. Standard equation of the circle. - PowerPoint PPT Presentation
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10.6 Equations of a Circle
Standard Equation of a Circle
Definition of a Circle
Definition of a Circle
A circle is a set of points a given distance from one point called the center.
The distance from the center is called the radius
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)
222 rkyhx
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
222 rkyhx
22 kyhxr
Write the equation of Circle
Center at ( -5,0) and radius 4.8
h =?
k =?
r = 4.8
222 rkyhx
Write the equation of Circle
Center at ( -5,0) and radius 4.8
h =-5
k =0
r = 4.8
222 rkyhx
04.235
8.405
22
222
yx
yx
Write the equation of Circle
Center at ( 4, -3) and a point on the circle (2,1)
h =k =r =x =y =
222 rkyhx
Write the equation of Circle
Center at ( 4, -3) and a point on the circle (2,1)
h = 4k = - 3r =x = 2y = 1
222 rkyhx
20164
42
3142
2
222
222
r
r
r
Write the equation of Circle
Center at ( 4, -3) and a point on the circle (2,1)
h = 4k = - 3r2 = 20x = 2y = 1
222 rkyhx
2034
203422
22
yx
yx
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)
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 then outside the circle.
Less then Inside the circle.
Equal is on the circle.
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)
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)
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
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)
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
Homework
Page 638 – 639
# 7 – 25 , 33 - 39
