# Equation Of Circle Worksheet

Math 2 Precalculus Algebra
Name________________________
Date_________________________
Circles — 2.4
(
)
(
)
(
)
=
2
+
2
d
x
x
y
y
1.
Use the distance formula
to write an equation of all of the coordinates
, x y
2
1
2
1
(
)
that are a distance, r, from the point
, h k and then illustrate this concept graphically.
Standard Form of the Equation of a Circle
The graph of circle is given by the equation:
(
)
(
)
2
+
2
=
2
x h
y k
r
,
(
)
where is the
, h k center of the circle and r is the radius of the circle.
Note:
(
)
+
=
2
2
2
x
y
r
If the center of the circle is
0 , 0 then the equation becomes
.
(
)
+
=
2
2
x
y
1
If the center of the circle is
0 , 0 and the radius is 1, then the equation becomes
. This circle is called the
unit circle.
General Form of the Equation of a Circle
The graph of circle may also be written by the equation:
+
+
+
+
=
2
2
x
y
ax
by
c
0
(
)
Write the standard form of the equation and the general form of the equation of the circle of radius r and center
, h k .
Graph the circle.
(
)
(
)
h k =
r =
2.
4
;
,
0 , 2