Find the Vertex Form x^2+y^2+2x-6y+7=0

Problem

x2+y2+2*x−6*y+7=0

Solution

1. Group the x terms and y terms together and move the constant term to the right side of the equation.

x2+2*x+y2−6*y=−7

2. Complete the square for the x terms by adding (2/2)2=1 to both sides.

x2+2*x+1+y2−6*y=−7+1

3. Complete the square for the y terms by adding ((−6)/2)2=9 to both sides.

x2+2*x+1+y2−6*y+9=−7+1+9

4. Factor the perfect square trinomials on the left side and simplify the constant on the right side.

(x+1)2+(y−3)2=4

Final Answer

x2+y2+2*x−6*y+7=0⇒(x+1)2+(y−3)2=4

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