1
Lesson 35
MA 152, Section 2.8
I
Circles
An earlier lesson has the distance and midpoint formulas.
You will need to
remember those formulas for this lesson.
2
2
2
1
2
1
1
2
1
2
(
)
(
)
:
,
2
2
d
x
x
y
y
x
x
y
y
M
=

+

+
+
A
circle
is a set of all points in a plane that are a fixed distance, called the
radius
, and
from a point called its
center.
Equation of a circle:
The distance formula can be used to find the equation of a circle.
Let the center of the circle be represented by the ordered pair (
h, k
) and the radius of the
circle by
r
.
Every point (
x, y
) is
r
units from (
h, k
).
2
2
2
2
2
)
(
)
(
)
(
)
(
k
y
h
x
r
k
y
h
x
r

+

=

+

=
This is the
standard equation for a circle.
Standard Equation of a Circle:
If the center of a circle is (
h, k
) and the radius of the circle is
r
units, the an equation for
the circle is
2
2
2
)
(
)
(
r
k
y
h
x
=

+

.
If the center of the circle is the origin, then the standard equation of the circle is
2
2
2
r
y
x
=
+
.
The
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