The document discusses equations of circles and how to find the equation given the center and radius or vice versa. It provides examples of finding the equation of circles with given centers and radii, as well as finding the center and radius from a given equation. It also shows how to find the equation of a circle if the center and a point on the circle are given.

1. JIM SMITH JCHS

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