Find the Center and Radius 3x^2+3y^2+6x-y=0

Problem

3*x2+3*y2+6*x−y=0

Solution

1. Divide the entire equation by 3 to make the coefficients of x2 and y2 equal to 1

x2+y2+2*x−1/3*y=0

2. Group the x terms and y terms together.

(x2+2*x)+(y2−1/3*y)=0

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

(x2+2*x+1)+(y2−1/3*y)=1

4. Complete the square for the y terms by adding ((−1/3)/2)2=1/36 to both sides.

(x2+2*x+1)+(y2−1/3*y+1/36)=1+1/36

5. Factor the trinomials into squared binomials and simplify the right side.

(x+1)2+(y−1/6)2=37/36

6. Identify the center (h,k) and radius r from the standard form (x−h)2+(y−k)2=r2

h=−1

k=1/6

r=√(,37/36)=√(,37)/6

Final Answer

Center: *(−1,1/6), Radius: √(,37)/6

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