Lesson: Circles in Graphs
The standard equation for
The standard equation for
the graph of a circle
The standard equation for
the graph of a circle
is (x-h)2 + (y-k)2 = r2
Standard equation for circle
(x-h)2 + (y-k)2 = r2
not (x-h)2 + (y-k)2 = r2
The center of the circle
The center of the circle
is (h,k)
The center of the circle
so for the equation (x+2)2 + (y-3)2 = 9
is (h,k)
The center of the circle
so for the equation (x+2)2 + (y-3)2 = 9
is (h,k)
the center is
The center of the circle
so for the equation (x+2)2 + (y-3)2 = 9
is (h,k)
the center is (-2
The center of the circle
so for the equation (x+2)2 + (y-3)2 = 9
is (h,k)
the center is (-2, 3)
The center of the circle
so for the equation (x+2)2 + (y-3)2 = 9
for the equation (x-1)2 + (y+6)2 = 25
is (h,k)
the center is (-2, 3)
The center of the circle
so for the equation (x+2)2 + (y-3)2 = 9
for the equation (x-1)2 + (y+6)2 = 25
is (h,k)
the center is (-2, 3)
the center is
The center of the circle
so for the equation (x+2)2 + (y-3)2 = 9
for the equation (x-1)2 + (y+6)2 = 25
is (h,k)
the center is (-2, 3)
the center is (1,
The center of the circle
so for the equation (x+2)2 + (y-3)2 = 9
for the equation (x-1)2 + (y+6)2 = 25
is (h,k)
the center is (-2, 3)
the center is (1,-6)
FInd the centers
(x+4)2 + (y-5)2 = 4
(x-2)2 + (y-5)2 = 4
(-4,5)
?
(2,5)
?
(x-6)2 + (y+2)2 = 4
x2 + (y+8)2 = 4
(6,-2)
?
(0,-8)
?
The radius of the circle
The radius of the circle
is the square root of the last number
The radius of the circle
is the square root of the last number
the radius of (x-2)2 + (y-5)2 = 25
The radius of the circle
is the square root of the last number
the radius of (x-2)2 + (y-5)2 = 25
is 5
The radius of the circle
is the square root of the last number
the radius of (x-3)2 + (y+6)2 = 9
the radius of (x-2)2 + (y-5)2 = 25
is 5
The radius of the circle
is the square root of the last number
the radius of (x-3)2 + (y+6)2 = 9
the radius of (x-2)2 + (y-5)2 = 25
is 3
is 5
Find the radius
(x-4)2 + (y+5)2 = 49
(x-2)2 + (y-5)2 = 16
7
?
4
?
(x-2)2 + y2 = 7
(x+1)2 + (y+6)2 = 4
√7
?
2
?
To graph a circle,
To graph a circle,
like this one
To graph a circle,
like this one
(x-11)2 + (y-3)2 = 4
To graph a circle,
like this one
(x-11)2 + (y-3)2 = 4
find the center and radius
To graph a circle,
like this one
(x-11)2 + (y-3)2 = 4
find the center and radius
Center (11,3)
To graph a circle,
like this one
(x-11)2 + (y-3)2 = 4
find the center and radius
Center (11,3)
radius = 2
To graph a circle,
like this one
(x-11)2 + (y-3)2 = 4
find the center and radius
Center (11,3)
then graph the center
radius = 2
To graph a circle,
like this one
(x-11)2 + (y-3)2 = 4
find the center and radius
Center (11,3)
then graph the center
radius = 2
To graph a circle,
like this one
(x-11)2 + (y-3)2 = 4
find the center and radius
Center (11,3)
then graph the center
radius = 2
To graph a circle,
like this one
(x-11)2 + (y-3)2 = 4
find the center and radius
Center (11,3)
then graph the center
radius = 2
To graph a circle,
like this one
(x-11)2 + (y-3)2 = 4
find the center and radius
Center (11,3)
then graph the center
radius = 2
then use the radius to
graph four points on
the circle
To graph a circle,
like this one
(x-11)2 + (y-3)2 = 4
find the center and radius
Center (11,3)
then graph the center
radius = 2
then use the radius to
graph four points on
the circle
Down 2
To graph a circle,
like this one
(x-11)2 + (y-3)2 = 4
find the center and radius
Center (11,3)
then graph the center
radius = 2
then use the radius to
graph four points on
the circle
Up 2
To graph a circle,
like this one
(x-11)2 + (y-3)2 = 4
find the center and radius
Center (11,3)
then graph the center
radius = 2
then use the radius to
graph four points on
the circle
Left 2
To graph a circle,
like this one
(x-11)2 + (y-3)2 = 4
find the center and radius
Center (11,3)
then graph the center
radius = 2
then use the radius to
graph four points on
the circle
Right 2
To graph a circle,
like this one
(x-11)2 + (y-3)2 = 4
find the center and radius
Center (11,3)
then graph the center
radius = 2
then use the radius to
graph four points on
the circle
(x-5)2 + (y+4)2 = 9
(x-5)2 + (y-4)2 = 9
(x-4)2 + (y-5)2 = 9
(x+4)2 + (y+5)2 = 9
(x-5)2 + (y+4)2 = 9
(x-5)2 + (y-4)2 = 9
(x-4)2 + (y-5)2 = 9
(x+4)2 + (y+5)2 = 4
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