Graph x^2+y^2-6x+2y-15

Math
x2+y2-6x+2y-15
Add 15 to both sides of the equation.
x2+y2-6x+2y=15
Complete the square for x2-6x.
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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)
Simplify the right side.
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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=-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.
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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.
(x-3)2-9
(x-3)2-9
Substitute (x-3)2-9 for x2-6x in the equation x2+y2-6x+2y=15.
(x-3)2-9+y2+2y=15
Move -9 to the right side of the equation by adding 9 to both sides.
(x-3)2+y2+2y=15+9
Complete the square for y2+2y.
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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.
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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.
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Simplify each term.
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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.
(y+1)2-1
(y+1)2-1
Substitute (y+1)2-1 for y2+2y in the equation x2+y2-6x+2y=15.
(x-3)2+(y+1)2-1=15+9
Move -1 to the right side of the equation by adding 1 to both sides.
(x-3)2+(y+1)2=15+9+1
Simplify 15+9+1.
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Add 15 and 9.
(x-3)2+(y+1)2=24+1
Add 24 and 1.
(x-3)2+(y+1)2=25
(x-3)2+(y+1)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=3
k=-1
The center of the circle is found at (h,k).
Center: (3,-1)
These values represent the important values for graphing and analyzing a circle.
Center: (3,-1)
Radius: 5
Graph x^2+y^2-6x+2y-15

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