Find the Center and Radius x^2+y^2+6y+2=0

Problem

x2+y2+6*y+2=0

Solution

1. Group the terms by variable and move the constant term to the right side of the equation.

x2+(y2+6*y)=−2

2. Complete the square for the y terms by taking half of the coefficient of y squaring it, and adding it to both sides.

6/2=3

3=9

x2+(y2+6*y+9)=−2+9

3. Factor the trinomial into a squared binomial and simplify the constant on the right side.

x2+(y+3)2=7

4. Identify the center and radius by comparing the equation to the standard form of a circle (x−h)2+(y−k)2=r2

h=0

k=−3

r2=7⇒r=√(,7)

Final Answer

Center: *(0,−3), Radius: √(,7)

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