Ch. 10.3 Circles

Report
Circles
Date: _____________
9.3 Circles
Circles
Standard Equation of a Circle
(x – h)2 + (y – k)2 = r2
center: (h, k)
radius: r
Write the equation of the circle that
whose center is at (-2,4) and
whose radius is 3.
( x  h)  ( y  k )  r
2
2
2
( x   2)  ( y  4)  3
2
2
( x  2)  ( y  4)  9
2
2
2
Write the equation of the circle that
whose center is at (-1,-6) and
whose radius is 6.
( x  h)  ( y  k )  r
2
2
2
( x   1)  ( y   6)  6
2
2
( x  1)  ( y  6)  36
2
2
2
Write the equation of the circle that
whose center is at (0,4) and whose
radius is 2.
( x  h)  ( y  k )  r
2
( x  0)  ( y  4)  2
2
2
2
2
2
x  ( y  4)  4
2
2
Find the center and radius of the
circle. Then write the equation of
the circle.
y
Center = (1,2)
Radius = 3
x
( x  1)  ( y  2)  3
2
2
( x  1)  ( y  2)  9
2
2
2
Find the center and radius of the
circle. Then write the equation of
the circle.
y
Center = (-1,0)
Radius = 4
x
( x   1)  ( y  0)  4
2
2
( x  1)  y  16
2
2
2
Find the center and radius of the
circle. Then graph the circle.
( x  1)  ( y  3)  16
2
Center = (-1,3)
2
y
Radius = 4
x
Find the center and radius of the
circle. Then graph the circle.
( x  3)  ( y  2)  4
2
Center = (-3,-2)
2
y
Radius = 2
x
Find the center and radius of the
circle. Then graph the circle.
( x  4)  ( y  1)  25
2
Center = (4,1)
2
y
Radius = 5
x
Complete the square.
x2 + 10x
1.
2.
3.
4.
5.
10  2 =5
52 = 25
x2 + 10x + 25
(x + 5)(x + 5)
(x + 5)2
Complete the square.
x2 – 20x
1.
2.
3.
4.
5.
-20  2 = -10
(-10)2 = 100
x2 – 20x + 100
(x – 10)(x – 10)
(x – 10)2
Completing the Square to Write
Standard Equations of Circles
1. Add/subtract to move the constant term
to the other side of the equation.
2. Rearrange the terms so that the x’s and
y’s are together.
3. Complete the square for the x’s and y’s.
4. Make sure that anything you added to
the one side of the equation is added to
the other side as well.
Write the equation of the circle in
standard form. Then find the center
and radius of the circle.
x2 + y2 + 4x – 6y – 3 = 0
x2 + y2 + 4x – 6y = 3
x2 + 4x + y2 – 6y = 3
4 + y2 – 6y + ___
9 = 3+ 4+ 9
x2 + 4x + ___
x2 + 4x + 4 + y2 – 6y + 9 = 16
(x + 2)2 + (y – 3)2 = 16
Center = (-2, 3)
Radius = 4
Write the equation of the circle in
standard form. Then find the center
and radius of the circle.
x2 + y2 – 12x – 2y – 8 = 0
x2 + y2 – 12x – 2y = 8
x2 – 12x + y2 – 2y = 8
36 + y2 – 2y + ___
1 = 8 +36 +1
x2 – 12x + ___
x2 – 12x + 36 + y2 – 2y + 1 = 45
(x – 6)2 + (y – 1)2 = 45
Center = (6, 1)
Radius = √45 ≈ 6.7
Write the equation of the circle in
standard form. Then find the center
and radius of the circle.
x2 + y2 – 10x + 4y + 17 = 0
x2 + y2 – 10x + 4y = -17
x2 – 10x + y2 + 4y = -17
25 + y2 + 4y + ___
4 = -17+25 +4
x2 – 10x + ___
x2 – 10x + 25 + y2 + 4y + 4 = 12
(x – 5)2 + (y + 2)2 = 12
Center = (5, -2)
Radius = √12 ≈ 3.5
Write the equation of the circle that passes
through the given point and has a center at the
origin.
y
(-5, -12)
d 
 x2
 x1  
d 
 5  0  
d 
 5
d 
25  144
d 
169
2
2
d  13
2

 y2
 y1 
2
 12  0 
 12 
2
x
2
x  y
2
2
 169

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