This document discusses circles in the coordinate plane. It defines the standard form of a circle equation as (x-h)2 + (y-k)2 = r2, where (h,k) are the coordinates of the center and r is the radius. Examples are given of identifying the center and radius from given equations and writing equations from given center and radius or a point on the circle. The steps for graphing a circle are outlined as plotting the center and drawing points at a distance of the radius from the center to form the circle.

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.
This means the radius can be found by
(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− + − =
Squaring both sides to
eliminate the square root
gives us the standard form of
a circle.

3. Examples
Identify the center and radius of the circles.
1.
2.
3.
( ) ( )
2 2
7 2 16x y− + − =
( ) ( )
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. 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.

6. 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)

7. 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+ + − =