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
x2+y2=r2
r is the radius
If the circle is not at the origin
 x  h
2
 y  k  r
2
The center is at (h, k)
2
Standard equation of the circle
If the circle is at the origin
x2+y2=r2
r is the radius
If the circle is not at the origin
 x  h
2
 y  k  r
2
Solve for r
r
 x  h
2
 y  k
2
2
Write the equation of Circle
Center at ( -5,0) and radius 4.8
 x  h
2
h =?
k =?
r = 4.8
 y  k  r
2
2
Write the equation of Circle
Center at ( -5,0) and radius 4.8
 x  h
2
h =-5
k =0
r = 4.8
 y  k  r
2
2
 x   5
  y  0  4.8
 x  5
2
2
2
2
 y  23.04
2
Write the equation of Circle
Center at ( 4, -3) and
a point on the circle (2,1)
 x  h
2
h=
k=
r=
x=
y=
 y  k  r
2
2
Write the equation of Circle
Center at ( 4, -3) and
a point on the circle (2,1)
 x  h
2
h=4
k=-3
r=
x=2
y=1
 y  k  r
2
2  4  1   3
 2  4  r
2
2
2
2
4  16  r  20
2
2
r
2
2
Write the equation of Circle
Center at ( 4, -3) and
a point on the circle (2,1)
 x  h
2
h=4
k=-3
r2 = 20
x=2
y=1
 x  4
 x  4
 y  k  r
2
2
2
  y   3  20
2
  y  3  20
2
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)
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
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