find the center and radius of the circle x2+y2+4x-21=0
Answers
Enter a problem...
Trigonometry Examples
Popular Problems Trigonometry Graph x^2+y^2+4x-2y-21=0
x
2
+
y
2
+
4
x
−
2
y
−
21
=
0
Add
21
to both sides of the equation.
x
2
+
y
2
+
4
x
−
2
y
=
21
Complete the square for
x
2
+
4
x
.
Tap for more steps...
(
x
+
2
)
2
−
4
Substitute
(
x
+
2
)
2
−
4
for
x
2
+
4
x
in the equation
x
2
+
y
2
+
4
x
−
2
y
=
21
.
(
x
+
2
)
2
−
4
+
y
2
−
2
y
=
21
Move
−
4
to the right side of the equation by adding
4
to both sides.
(
x
+
2
)
2
+
y
2
−
2
y
=
21
+
4
Complete the square for
y
−
2
y
.
(
y
−
1
)
2
−
1
Substitute
(
y
−
1
)
2
−
1
for
y
2
−
2
y
in the equation
x
2
+
y
2
+
4
x
−
2
y
=
21
.
(
x
+
2
)
2
+
(
y
−
1
)
2
−
1
=
21
+
4
Move
−
1
to the right side of the equation by adding
1
to both sides.
(
x
+
2
)
2
+
(
y
−
1
)
2
=
21
+
4
+
1
Simplify
21
+
4
+
1
.
(
x
+
2
)
2
+
(
y
−
1
)
2
=
26
This is the form of a circle. Use this form to determine the center and radius of the circle.
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
Match the values in this circle to those of the standard form. The variable
r
represents the radius of the circle,
h
represents the x-offset from the origin, and
k
represents the y-offset from origin.
r
=
√
26
h
=
−
2
k
=
1
The center of the circle is found at
(
h
,
k
)
.
Center:
(
−
2
,
1
)
These values represent the important values for graphing and analyzing a circle.
Center:
(
−
2
,
1
)
Radius:
√
26