Equation of a Circle
A point (
x
,
y
) is on a circle if and only if its distance from the center (
a
,
b
) is
r
.
From the
distance formula
the following equation results:
(Eq1)
r
= √
(
x
−
a
)
2
+ (
y
−
b
)
2
The point (
x
,
y
) lies on a circle of radius
r
and center (
a
,
b
) if and only if:
(Eq2)
(
x
−
a
)
2
+ (
y
−
b
)
2
=
r
2
This equation represents the standard form of the equation of a circle, where the equation is obtained by squaring both sides of Eq1.
Therefore, the standard form of the equation of a circle with its center at the origin, (
a
,
b
) = (0, 0), is:
x
2
+
y
2
=
r
2
