Graph x^2+y^2-10x+6y+27=0

Math
x2+y2-10x+6y+27=0
Subtract 27 from both sides of the equation.
x2+y2-10x+6y=-27
Complete the square for x2-10x.
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Use the form ax2+bx+c, to find the values of a, b, and c.
a=1,b=-10,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=-102(1)
Simplify the right side.
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Cancel the common factor of 10 and 2.
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Factor 2 out of 10.
d=-2⋅52⋅1
Cancel the common factors.
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Factor 2 out of 2⋅1.
d=-2⋅52(1)
Cancel the common factor.
d=-2⋅52⋅1
Rewrite the expression.
d=-51
Divide 5 by 1.
d=-1⋅5
d=-1⋅5
d=-1⋅5
Multiply -1 by 5.
d=-5
d=-5
Find the value of e using the formula e=c-b24a.
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Simplify each term.
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Raise -10 to the power of 2.
e=0-1004⋅1
Multiply 4 by 1.
e=0-1004
Divide 100 by 4.
e=0-1⋅25
Multiply -1 by 25.
e=0-25
e=0-25
Subtract 25 from 0.
e=-25
e=-25
Substitute the values of a, d, and e into the vertex form a(x+d)2+e.
(x-5)2-25
(x-5)2-25
Substitute (x-5)2-25 for x2-10x in the equation x2+y2-10x+6y=-27.
(x-5)2-25+y2+6y=-27
Move -25 to the right side of the equation by adding 25 to both sides.
(x-5)2+y2+6y=-27+25
Complete the square for y2+6y.
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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)
Cancel the common factor of 6 and 2.
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Factor 2 out of 6.
d=2⋅32⋅1
Cancel the common factors.
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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=3
d=3
d=3
Find the value of e using the formula e=c-b24a.
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Simplify each term.
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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.
(y+3)2-9
(y+3)2-9
Substitute (y+3)2-9 for y2+6y in the equation x2+y2-10x+6y=-27.
(x-5)2+(y+3)2-9=-27+25
Move -9 to the right side of the equation by adding 9 to both sides.
(x-5)2+(y+3)2=-27+25+9
Simplify -27+25+9.
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Add -27 and 25.
(x-5)2+(y+3)2=-2+9
Add -2 and 9.
(x-5)2+(y+3)2=7
(x-5)2+(y+3)2=7
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=7
h=5
k=-3
The center of the circle is found at (h,k).
Center: (5,-3)
These values represent the important values for graphing and analyzing a circle.
Center: (5,-3)
Radius: 7
Graph x^2+y^2-10x+6y+27=0

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