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Circle
Circle. Center of circle. Radius
of circle.
Equation of circle. Equation of
tangent line to circle.
Tangency condition of straight
line and circle.
A
circle
(
Fig.1
)
is
a
locus
of
points,
equidistant from the given point Î,
called a center of circle, at the distance R. A number
R > 0 is called a radius of circle.
An equation of circle
of radius R
with a center in a point
Î
( õ0
, ó
0
) is:
(
õ
– õ0
)
2
+ (
ó
– ó 0
)
2 =
R 2
.
If a center of the circle
coincides with the origin of coordinates, then an equation of circle becomes:
õ
2
+ ó
2 =
R 2
.
Let
Ð
(
õ1
,
ó
1
) be a point of the circle (
Fig.1
), then an equation of tangent
line to circle
in the given point is:
(
õ1
– õ0
)
( õ
– õ0
)
+
(
ó1
– ó
0
) (
ó
– ó
0
) = R
2 .
A tangency condition of a
straight line y
= m
x
+ k and a circle õ
2
+
ó
2 = R
2 :
k 2 / (
1 + m 2
) = R 2
.
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