X²+y²-8x+6y+9=0, find the centre and the radius of this circle.
Answers
Answered by
5
Complete the square for
x
and
y
and rearrange:
0
=
x
2
+
y
2
−
8
x
−
6
y
−
75
=
(
x
2
−
8
x
+
16
)
+
(
y
2
−
6
y
+
9
)
−
100
=
(
x
−
4
)
2
+
(
y
−
3
)
2
−
10
2
Add
10
2
to both ends and transpose to get:
(
x
−
4
)
2
+
(
y
−
3
)
2
=
10
2
This is in the standard form of the equation of a circle:
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
where
(
h
,
k
)
=
(
4
,
3
)
is the centre of the circle and
r
=
10
is the radius.
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