find the radius of the circle whose center is 3, 2 passes throgh -5 , 6
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Answer:
The general form of the equation of a circle is
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
where
(
h
,
k
)
are the coordinates of the center and
r
is the length of the radius.
We are given that the center is at
(
2
,
6
)
so we need to figure out the length of the radius. Since we know the circle passes through the point
(
3
,
1
)
, we know the radius is just the distance between
(
2
,
6
)
and
(
3
,
1
)
. In the equation, we end up using
r
2
instead of
r
which makes our calculations a bit easier:
Distance
=
r
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
r
2
=
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
r
2
=
(
2
−
3
)
2
+
(
6
−
1
)
2
r
2
=
26
Now that we have everything, we just substitute our values into the equation of a circle:
(
x
−
2
)
2
+
(
y
−
6
)
2
=
26
Step-by-step explanation:
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