standard form of a circle center is at (h, k) r is the radius of the circle
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Standard Form of a Circle
Center is at (h, k) 2 2 2x h y k r
r is the radius of the circle
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Every binomial squared has been multiplied out.
Every term is on the left side, equal to 0.
2 2: 4 6 3 0 Example x y x y
General Form of a Circle
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EX 1 Write an equation of a circle with center (3, -2) and a radius of 4.
2 2 2+x h y k r
(x ) (y )2 2 3 2 42( )
(x ) (y )2 2 3 2 16
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EX 2 Write an equation of a circle with center (-4, 0) and a diameter of 10.
(x ) (y )2 2 h k r 2
(x ) (y2 2 ( ) )4 0 52
(x ) y2 2 4 25
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EX 3 Write an equation of a circle with center (2, -9) and a radius of .
(x ) (y )2 2 h k r 2
11
2222 9 11x y
2 22 9 11x y
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EX 4 Find the coordinates of the center and the measure of the radius.
(x ) (y +2 2 6 3 25)
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The center is
The radius is
The equation is
5. Find the center, radius, & equation of the circle.
(0, 0)
12
x2 + y2 = 144
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The center is
The radius is
The equation is
6. Find the center, radius, & equation of the circle.
(1, -3)
7
(x – 1)2 + (y + 3)2 = 49
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7. Graph the Circle
(x – 3)2 + (y – 2)2 = 9
Center (3, 2)
Radius of 3
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Converting from General to Standard
1.Move the x terms together and the y terms together.
2.Complete the square (as needed) for x.
3.Complete the square(as needed) for y.
4.Factor the left & simplify the right
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2 2( 8 ) 7 x x y
8. Write the standard equation of the circle. State the center & radius.
2 2 8 7 0x y x
Center: (4, 0) radius: 3
2 2( 4) 9x y
2 2( 8 )16 167 x x y
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2 24 6 3 x x y y
9. Write the standard equation of the circle. State the center & radius.
2 2 4 6 3 0 x y x y
Center: (-2, 3) radius: 4
2 22 3 16 x y
2 24 6 9394 4 x x y y
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2 28 2 10 x x y y
10. Write the standard equation of the circle. State the center & radius.
2 22 2 16 4 20 0 x y x y
2 24 1 7 x y
2 28 2 1 116 1610 x x y y
2 2 8 2 10 0 x y x y
: (4, 1) : 7 2.6 Center Radius
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11. Write the general form of the equation of the circle.
2 24 3 36 x y
2 28 16 6 9 36 x x y y2 28 16 6 9 36 0 x x y y
2 2 8 6 11 0 x y x y
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HomeworkWorksheet
17 problems