Centre of the conic 5x + xy + 5y2 - 10x - y - 3-0 is at point
Answers
Answer:
The center of this circle is
(
−
1
,
3
)
and radius
1
√
5
Explanation:
The general form of the equation of a circle is :
(
x
−
a
)
2
+
(
y
−
b
)
2
=
r
2
where
(
a
,
b
)
is the center of the circle and
r
is its radius.
In the given exercise we are asked to transform this standard form
into the general form of the equation of a circle.
First , the coefficients of
x
2
and
y
2
should be equal to
1
.
Then, complete the square.
5
x
2
+
5
y
2
+
10
x
−
30
y
+
49
=
0
⇒
5
x
2
+
5
y
2
+
10
x
−
30
y
+
49
5
=
0
5
⇒
x
2
+
y
2
+
2
x
−
6
y
+
49
5
=
0
⇒
(
x
2
+
2
x
+
1
)
+
(
y
2
−
6
y
+
9
)
+
(
49
5
−
1
−
9
)
=
0
⇒
(
x
2
+
2
x
+
1
)
+
(
y
2
−
6
y
+
9
)
+
(
49
5
−
5
5
−
45
5
)
=
0
⇒
(
x
2
+
2
x
+
1
)
+
(
y
2
−
6
y
+
9
)
+
(
−
1
5
)
=
0
⇒
(
x
+
1
)
2
+
(
y
−
3
)
2
=
1
5
The equation of the circle is:
(
x
+
1
)
2
+
(
y
−
3
)
2
=
(
1
√
5
)
2
Hence, The center of this circle is
(
−
1
,
3
)
and radius
1
√
5
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