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EQUATIONS OF CIRCLES

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**THE EQUATION OF A CIRCLE ON A GRAPH CAN BE DEFINED AS**

( x - h )² + ( y – k )² = r² ( h , k ) = center r = radius

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**IF YOU HAVE THE CENTER AND RADIUS**

OF A CIRCLE, PLUG IN TO FIND THE EQUATION. Center = ( 3 , 6 ) radius = 4 h , k r ( x - h )² + ( y – k )² = r² ( x - 3 )² + ( y – 6 )² = 4² ( x - 3 )² + ( y – 6 )² = 16

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**IF YOU HAVE THE CENTER AND RADIUS**

OF A CIRCLE, PLUG IN TO FIND THE EQUATION. Center = ( -5 , 0 ) radius = 8 h , k r ( x - h )² + ( y – k )² = r² ( x - -5 )² + ( y – 0 )² = 8² ( x + 5 )² + y ² = 64

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**FIND THE EQUATION OF THE CIRCLE**

Center At ( 3 , 9 ) Radius = 5 ( x - 3 )² + ( y - 9 )² = 25 Center At ( -5 , 3 ) Radius = 2 (X + 5) ² + ( y - 3 )² = 4 Center At ( 0 , 0 ) Radius = 17 x ² + y ² = 289

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**IF YOU HAVE THE EQUATION OF A CIRCLE, UNPLUG TO FIND THE**

CENTER AND RADIUS. ( x - h )² + ( y – k )² = r² ( h , k ) = center r = radius ( x - 7 )² + ( y – 1 )² = 36 Center = 7 , 1 Radius = 36 = 6

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**( x + 2 )² + ( y + 9 )² = 17 ( x – (- 2 ) )² + ( y - ( -9 ) )² = 17**

IF YOU HAVE THE EQUATION OF A CIRCLE, UNPLUG TO FIND THE CENTER AND RADIUS. ( x - h )² + ( y – k )² = r² ( h , k ) = center r = radius ( x + 2 )² + ( y + 9 )² = 17 ( x – (- 2 ) )² + ( y - ( -9 ) )² = 17 Center = -2 , -9 Radius = 17

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**FIND THE CENTER AND RADIUS**

OF EACH CIRCLE ( x – 11 )² + ( y – 8 )² = 25 Center = ( 11,8 ) Radius = 5 ( x – 3 )² + ( y + 1 )² = 81 Center = ( 3,-1 ) Radius = 9 ( x + 6 )² + y ² = 21 Center = ( -6,0 ) Radius = 21

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**If A Circle Has A Center At ( 2 , 4) And Passes Through (4 , 8 ), **

YOU NEED TO KNOW THE CENTER AND RADIUS TO FIND THE EQUATION OF A CIRCLE. If A Circle Has A Center At ( 2 , 4) And Passes Through (4 , 8 ), What Is The Equation Of The Circle?

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**( x - 2 )² + ( y - 4 )² = 20 r = (x-x)² + (y-y)²**

Center At ( 2 , 4) Passes Through (4 , 8 ) ( x - 2 )² + ( y - 4 )² = r² The Radius Is The Distance From The Center To A Point On The Circle. r = (x-x)² + (y-y)² r = ( 4 – 2 )² + ( 8 – 4 )² r = 2² + 4² = 20 ( x - 2 )² + ( y - 4 )² = 20 ² ( x - 2 )² + ( y - 4 )² = 20

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**FIND THE EQUATION OF THE CIRCLE**

Center At ( 3 , 6 ) Passes Through ( 1 , 5 ) ( x - 3 )² + ( y - 6 )² = 5 Center At ( 0 , 5 ) Passes Through ( 6 , 2 ) x ² + ( y - 5 )² = 45 Center At ( -3 , 1 ) Passes Through (-4 , -4 ) ( x + 3 )² + ( y – 1 )² = 26

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