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
( õ_{0}
, ó_{
0}
) is:
(
õ
– õ_{0 }
)
^{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
(
õ_{1}
,
ó_{
1}
) be a point of the circle (
Fig.1
), then an equation of tangent
line to circle
in the given point is:
(
õ_{1}
– õ_{0
})
( õ
– õ_{0
})
^{ }+
(
ó_{1}
– 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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