# Graph x^2+y^2+2x+4y-20=0

x2+y2+2x+4y-20=0
Add 20 to both sides of the equation.
x2+y2+2x+4y=20
Complete the square for x2+2x.
Use the form ax2+bx+c, to find the values of a, b, and c.
a=1,b=2,c=0
Consider the vertex form of a parabola.
a(x+d)2+e
Substitute the values of a and b into the formula d=b2a.
d=22(1)
Cancel the common factor of 2.
Cancel the common factor.
d=22⋅1
Divide 1 by 1.
d=1
d=1
Find the value of e using the formula e=c-b24a.
Simplify each term.
Raise 2 to the power of 2.
e=0-44⋅1
Multiply 4 by 1.
e=0-44
Divide 4 by 4.
e=0-1⋅1
Multiply -1 by 1.
e=0-1
e=0-1
Subtract 1 from 0.
e=-1
e=-1
Substitute the values of a, d, and e into the vertex form a(x+d)2+e.
(x+1)2-1
(x+1)2-1
Substitute (x+1)2-1 for x2+2x in the equation x2+y2+2x+4y=20.
(x+1)2-1+y2+4y=20
Move -1 to the right side of the equation by adding 1 to both sides.
(x+1)2+y2+4y=20+1
Complete the square for y2+4y.
Use the form ax2+bx+c, to find the values of a, b, and c.
a=1,b=4,c=0
Consider the vertex form of a parabola.
a(x+d)2+e
Substitute the values of a and b into the formula d=b2a.
d=42(1)
Cancel the common factor of 4 and 2.
Factor 2 out of 4.
d=2⋅22⋅1
Cancel the common factors.
Factor 2 out of 2⋅1.
d=2⋅22(1)
Cancel the common factor.
d=2⋅22⋅1
Rewrite the expression.
d=21
Divide 2 by 1.
d=2
d=2
d=2
Find the value of e using the formula e=c-b24a.
Simplify each term.
Cancel the common factor of (4)2 and 4.
Factor 4 out of (4)2.
e=0-4⋅44(1)
Cancel the common factors.
Cancel the common factor.
e=0-4⋅44⋅1
Rewrite the expression.
e=0-41
Divide 4 by 1.
e=0-1⋅4
e=0-1⋅4
e=0-1⋅4
Multiply -1 by 4.
e=0-4
e=0-4
Subtract 4 from 0.
e=-4
e=-4
Substitute the values of a, d, and e into the vertex form a(x+d)2+e.
(y+2)2-4
(y+2)2-4
Substitute (y+2)2-4 for y2+4y in the equation x2+y2+2x+4y=20.
(x+1)2+(y+2)2-4=20+1
Move -4 to the right side of the equation by adding 4 to both sides.
(x+1)2+(y+2)2=20+1+4
Simplify 20+1+4.
(x+1)2+(y+2)2=21+4
(x+1)2+(y+2)2=25
(x+1)2+(y+2)2=25
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=r2
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=5
h=-1
k=-2
The center of the circle is found at (h,k).
Center: (-1,-2)
These values represent the important values for graphing and analyzing a circle.
Center: (-1,-2)