1. EQUATIONS OF CIRCLES

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

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. ( 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

8. 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

9. 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?

10. ( 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

11. 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