x2+y2-6x-8y-11=0

Add 11 to both sides of the equation.

x2+y2-6x-8y=11

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

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

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)

Radius: 6

Graph x^2+y^2-6x-8y-11=0