CIRCLES
Unit 3-2
Equations we’ll need:

Distance formula
d

 x1  x2    y1  y2 
2
2
Midpoint formula
 x1  x2 y1  y2 
M  ( x, y )  
,

2 
 2
Definitions

Circle: Set of all points in a plane that is a
fixed distance from a fixed point

Center: The fixed equidistance point of the
circle

Radius: The fixed equidistance length of the
circle
Circle Equation
( x  h)  ( y  k )  r
2
Center  (h, k )
Radius  r
2
2
Example 1

Name the center and the radius of this circle,
( x  2)2  ( y  3)2  16 and graph it
( x  h)  ( y  k )  r
2
r  16
r4
2
2
2
c  (2,3)
r4
Example 1

Name the center and the radius of this circle,
( x  2)2  ( y  3)2  16 and graph it
( x  2)  ( y  3)  4
2
c  (2,3)
r4
2
2
Example 2
Write an equation of the circle with its center at
(–3, 5), the radius is 5 and graph it.
( x  h)  ( y  k )  r
2
2
2
Example 3
Name the center and the radius of this circle,
x 2  y 2  25 and graph it
( x  h)  ( y  k )  r
2
2
2
YOUR TURN!
Graph the equation ( x  3)2  ( y  2)2  9
( x  h)  ( y  k )  r
2
Example 4
2
2
Find the radius, graph the circle, and write the
equation in standard form with the given center of
(2, -3) and the point (1, 0).
 x1  x2    y1  y2 
2
d
d
 2 1   3  0
2
d
1   3
2
2
radius
2
d  1  9  10
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2
radius
2.3 - Circles
C
10
( x  h)  ( y  k )  r
2
Example 4
2
2
Find the radius, graph the circle, and write the
equation in standard form with the given center of
(2, -3) and the point (1, 0).
r  10
C  (2, 3)
( x  2)  ( y  (3)) 
2
2
 10 
2
( x  2)  ( y  3)  10
2
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radius =
10
2
C
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11
Example 5
( x  h)  ( y  k )  r
2
2
2
Write a circle equation whose center is at the
origin and passes through (1, –6).
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12
YOUR TURN!
( x  h)  ( y  k )  r
2
2
2
Write a circle equation whose center is at (1, 0)
and passes through (-2, 3)
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Example 6
( x  h)  ( y  k )  r
Write a circle equation whose endpoints of a
diameter are (-5, 2) and (3, 6).
2
2
2
 x  x y  y2 
MP   1 2 , 1

2 
 2
 5  3 2  6 
MP  
,

2 
 2
Diameter
MP   1, 4 
Center
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14
Example 6
( x  h)  ( y  k )  r
Write a circle equation whose endpoints of a
diameter are (-5, 2) and (3, 6).
2
2
MP   1, 4 
2
d
 x1  x2    y1  y2 
d
 5  (1)    2  4
d
 4   2
2
2
2
d  16  4  20
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Radius
Center
2
Center
2
2
Radius
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15
Example 6
( x  h)  ( y  k )  r
Write a circle equation whose endpoints of a
diameter are (-5, 2) and (3, 6).
2
2
2
r  20
C  (1, 4)
( x  (1))  ( y  4) 
2
2

20

2
( x  1)  ( y  4)  20
2
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2
2.3 - Circles
16
d
YOUR TURN!
 x1  x2    y1  y2 
2
2
 x1  x2 y1  y2 
MP  
,

2 
 2
( x  h)  ( y  k )  r
Write a circle equation whose endpoints of a
diameter are (5, 4) and (-1, -6).
2
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2
2
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17
Example 7
Determine the equation of this circle by the
graph given
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18
YOUR TURN!
Determine the equation of this circle by the
graph given
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19
Assignment
WORKSHEET!
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20