Lesson 35
MA 15200, Section 2.8
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
general equation for a circle
is an equation where the parentheses are cleared from
the standard form (binomials are squared)
.
General Equation of a Circle:
numbers.
real
represent
and
,
,
where
,
0
2
2
e
d
c
e
dy
cx
y
x
=
+
+
+
+
Ex 1:
Find the standard equation and general form of each circle described.
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 Spring '09
 Distance Formula, Quadratic equation

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