# Graph x^2+y^2-14x+12y+49=0 x2+y2-14x+12y+49=0
Subtract 49 from both sides of the equation.
x2+y2-14x+12y=-49
Complete the square for x2-14x.
Use the form ax2+bx+c, to find the values of a, b, and c.
a=1,b=-14,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=-142(1)
Simplify the right side.
Cancel the common factor of 14 and 2.
Factor 2 out of 14.
d=-2⋅72⋅1
Cancel the common factors.
Factor 2 out of 2⋅1.
d=-2⋅72(1)
Cancel the common factor.
d=-2⋅72⋅1
Rewrite the expression.
d=-71
Divide 7 by 1.
d=-1⋅7
d=-1⋅7
d=-1⋅7
Multiply -1 by 7.
d=-7
d=-7
Find the value of e using the formula e=c-b24a.
Simplify each term.
Raise -14 to the power of 2.
e=0-1964⋅1
Multiply 4 by 1.
e=0-1964
Divide 196 by 4.
e=0-1⋅49
Multiply -1 by 49.
e=0-49
e=0-49
Subtract 49 from 0.
e=-49
e=-49
Substitute the values of a, d, and e into the vertex form a(x+d)2+e.
(x-7)2-49
(x-7)2-49
Substitute (x-7)2-49 for x2-14x in the equation x2+y2-14x+12y=-49.
(x-7)2-49+y2+12y=-49
Move -49 to the right side of the equation by adding 49 to both sides.
(x-7)2+y2+12y=-49+49
Complete the square for y2+12y.
Use the form ax2+bx+c, to find the values of a, b, and c.
a=1,b=12,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=122(1)
Cancel the common factor of 12 and 2.
Factor 2 out of 12.
d=2⋅62⋅1
Cancel the common factors.
Factor 2 out of 2⋅1.
d=2⋅62(1)
Cancel the common factor.
d=2⋅62⋅1
Rewrite the expression.
d=61
Divide 6 by 1.
d=6
d=6
d=6
Find the value of e using the formula e=c-b24a.
Simplify each term.
Raise 12 to the power of 2.
e=0-1444⋅1
Multiply 4 by 1.
e=0-1444
Divide 144 by 4.
e=0-1⋅36
Multiply -1 by 36.
e=0-36
e=0-36
Subtract 36 from 0.
e=-36
e=-36
Substitute the values of a, d, and e into the vertex form a(x+d)2+e.
(y+6)2-36
(y+6)2-36
Substitute (y+6)2-36 for y2+12y in the equation x2+y2-14x+12y=-49.
(x-7)2+(y+6)2-36=-49+49
Move -36 to the right side of the equation by adding 36 to both sides.
(x-7)2+(y+6)2=-49+49+36
Simplify -49+49+36.
Add -49 and 49.
(x-7)2+(y+6)2=0+36
Add 0 and 36.
(x-7)2+(y+6)2=36
(x-7)2+(y+6)2=36
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=6
h=7
k=-6
The center of the circle is found at (h,k).
Center: (7,-6)
These values represent the important values for graphing and analyzing a circle.
Center: (7,-6)     