The document explains how to write equations and graph circles in the coordinate plane, emphasizing the use of the distance formula. It provides examples of identifying the center and radius of circles, as well as instructions for graphing them. Students learn to plot the center, measure the radius, and connect points to form a circle or use a compass for accuracy.

1. Circles in the Coordinate Plane
The student is able to (I can):
• Write equations and graph circles in the coordinate plane
• Use the equation and graph of a circle to solve problems.

2. The equation of a circle is based on the Distance Formula.
(h, k)
(x, y)
r
( ) ( )
2 2
2 1 2 1d x x y y= − + −
( ) ( )
2 2
r x h y k= − + −
( ) ( )
2 2 2
x h y k r− + − =

3. Examples
Identify the center and radius of the circles.
1.
center: (7, 2); radius:
2.
3.
( ) ( )
2 2
7 2 16x y− + − =
16 4=
( ) ( )
2 2
5 1 36x y+ + − =
( )
22
3 20x y+ + =

4. Examples
Identify the center and radius of the circles.
1.
center: (7, 2); radius:
2.
center: (–5, 1); radius:
3.
center: (0, –3); radius:
( ) ( )
2 2
7 2 16x y− + − =
16 4=
( ) ( )
2 2
5 1 36x y+ + − =
36 6=
( )
22
3 20x y+ + =
20 2 5=

5. Examples
Write the equation of each circle.
1. ⊙A with center A(4, –2) and radius 3
2. ⊙B with center B(–6, 3) that passes through (–2, 6)
( ) ( )( )
22 2
4 2 3x y− + − − =
h k
( ) ( )
2 2
4 2 9x y− + + =
h k x y
( )( ) ( )
2 2 2
2 66 3 r−− + − =−
2
25 r=
( ) ( )
2 2
6 3 25x y+ + − =

6. To graph a circle once you know its center and radius:
• Plot its center
• Count the radius from the center up, down, left, and right.
• Draw a smooth curve connecting the four points.
You can also use a compass. Plot the center as before, open
up the compass to the length of the radius, and then draw
the circle.