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Find the radius and the center of the given equations of;
1. x² + y² = 144
2. x + y - 12× - 12y = 144
Find the radius and the center of the given equations of;
1. x² + y² = 144
2. x + y - 12× - 12y = 144
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2.)The center is
(
2
,
−
6
)
and the radius is
2
√
19
Explanation:
x
2
+
y
2
−
4
x
+
12
y
−
36
=
0
Rearrange the terms by grouping the x terms, grouping the y terms, and moving the constant term to the other side
x
2
−
4
x
a
a
a
+
y
2
+
12
y
a
a
a
=
36
a
a
a
Complete the square for x terms and the y terms.
To complete the square for the x terms, divide the coefficient of the "middle term"
4
x
by 2, square the result to get
4
and add
4
to both sides of the equation.
x
2
−
4
x
+
4
a
a
a
+
y
2
+
12
y
a
a
=
36
+
4
To complete the square for the y terms, divide the coefficient of the "middle term"
12
y
by 2, square the result to get
36
and add
36
to both sides of the equation.
x
2
−
4
x
+
4
a
a
a
+
y
2
+
12
y
+
36
=
36
+
4
+
36
x
2
−
4
x
+
4
a
a
a
+
y
2
+
12
y
+
36
=
76
Factor each group of terms.
(
x
−
2
)
(
x
−
2
)
+
(
y
+
6
)
(
y
+
6
)
=
76
(
x
−
2
)
2
+
(
y
+
6
)
2
=
76
This equation of a circle is
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
where
(
h
,
k
)
is the center and
r
is the radius.
Thus the center is
(
2
,
−
6
)
and the radius is
√
76
or
2
√
19