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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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Presentation on theme: "THE EQUATION OF A CIRCLE ON A GRAPH CAN BE DEFINED AS ( x - h )² + ( y – k )² = r² ( h, k ) = center r = radius."— Presentation transcript:

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2 THE EQUATION OF A CIRCLE ON A GRAPH CAN BE DEFINED AS ( x - h )² + ( y – k )² = r² ( h, k ) = center r = radius

3 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

4 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

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

6 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

7 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

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

9 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?

10 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

11 FIND THE EQUATION OF THE CIRCLE Center At ( 3, 6 ) Passes Through ( 1, 5 ) Center At ( 0, 5 ) Passes Through ( 6, 2 ) Center At ( -3, 1 ) Passes Through (-4, -4 ) ( x - 3 )² + ( y - 6 )² = 5 x ² + ( y - 5 )² = 45 ( x + 3 )² + ( y – 1 )² = 26


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