find center and radius of 2x+2y=-x-y=0
Answers
Answer:
How do you find the center and radius of the circle
x
2
−
2
x
+
y
2
−
8
y
+
1
=
0
?
Precalculus Identify Critical Points
2 Answers
Noah G
Dec 19, 2016
Radius:
4
Centre:
(
−
1
,
4
)
Explanation:
You should convert to the form
(
x
−
a
)
2
+
(
y
−
b
)
2
=
r
2
. Complete the square twice to achieve this.
1
(
x
2
−
2
x
+
n
)
+
1
(
y
2
−
8
y
+
m
)
=
−
1
Our goal here is to make the expressions in parentheses into perfect squares. We can use the formula
n
=
(
b
2
)
2
and
m
=
(
b
2
)
2
, where
b
is the x-coefficent term.
So,
n
=
(
−
2
2
)
2
=
1
m
=
(
−
8
2
)
2
=
16
We need to add and subtract this number inside the parentheses to keep the equation equivalent.
1
(
x
2
−
2
x
+
1
−
1
)
+
1
(
y
2
−
8
x
+
16
−
16
)
=
−
1
1
(
x
2
−
2
x
+
1
)
−
1
+
1
(
y
2
−
8
x
+
16
)
−
16
=
−
1
(
x
−
1
)
2
+
(
y
−
4
)
2
=
−
1
+
17
(
x
+
1
)
2
+
(
y
−
4
)
2
=
16
The radius of a circle in the form
(
x
−
a
)
2
+
(
y
−
b
)
2
=
r
2
is
r
, so in this case
4
. The centre is at
(
a
,
b
)
, in this case
(
−
1
,
4
)
.
Hopefully this helps!