# Graph x^2+y^2-6x-8y-11=0 x2+y2-6x-8y-11=0
Add 11 to both sides of the equation.
x2+y2-6x-8y=11
Complete the square for x2-6x.
Use the form ax2+bx+c, to find the values of a, b, and c.
a=1,b=-6,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=-62(1)
Simplify the right side.
Cancel the common factor of 6 and 2.
Factor 2 out of 6.
d=-2⋅32⋅1
Cancel the common factors.
Factor 2 out of 2⋅1.
d=-2⋅32(1)
Cancel the common factor.
d=-2⋅32⋅1
Rewrite the expression.
d=-31
Divide 3 by 1.
d=-1⋅3
d=-1⋅3
d=-1⋅3
Multiply -1 by 3.
d=-3
d=-3
Find the value of e using the formula e=c-b24a.
Simplify each term.
Raise -6 to the power of 2.
e=0-364⋅1
Multiply 4 by 1.
e=0-364
Divide 36 by 4.
e=0-1⋅9
Multiply -1 by 9.
e=0-9
e=0-9
Subtract 9 from 0.
e=-9
e=-9
Substitute the values of a, d, and e into the vertex form a(x+d)2+e.
(x-3)2-9
(x-3)2-9
Substitute (x-3)2-9 for x2-6x in the equation x2+y2-6x-8y=11.
(x-3)2-9+y2-8y=11
Move -9 to the right side of the equation by adding 9 to both sides.
(x-3)2+y2-8y=11+9
Complete the square for y2-8y.
Use the form ax2+bx+c, to find the values of a, b, and c.
a=1,b=-8,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=-82(1)
Simplify the right side.
Cancel the common factor of 8 and 2.
Factor 2 out of 8.
d=-2⋅42⋅1
Cancel the common factors.
Factor 2 out of 2⋅1.
d=-2⋅42(1)
Cancel the common factor.
d=-2⋅42⋅1
Rewrite the expression.
d=-41
Divide 4 by 1.
d=-1⋅4
d=-1⋅4
d=-1⋅4
Multiply -1 by 4.
d=-4
d=-4
Find the value of e using the formula e=c-b24a.
Simplify each term.
Raise -8 to the power of 2.
e=0-644⋅1
Multiply 4 by 1.
e=0-644
Divide 64 by 4.
e=0-1⋅16
Multiply -1 by 16.
e=0-16
e=0-16
Subtract 16 from 0.
e=-16
e=-16
Substitute the values of a, d, and e into the vertex form a(x+d)2+e.
(y-4)2-16
(y-4)2-16
Substitute (y-4)2-16 for y2-8y in the equation x2+y2-6x-8y=11.
(x-3)2+(y-4)2-16=11+9
Move -16 to the right side of the equation by adding 16 to both sides.
(x-3)2+(y-4)2=11+9+16
Simplify 11+9+16.
Add 11 and 9.
(x-3)2+(y-4)2=20+16
Add 20 and 16.
(x-3)2+(y-4)2=36
(x-3)2+(y-4)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=3
k=4
The center of the circle is found at (h,k).
Center: (3,4)
These values represent the important values for graphing and analyzing a circle.
Center: (3,4)     