Do a double completion of square, with respect to xx and yy, in order to convert to the arm (x - a)^2 + (y - b)^2 = r(x−a)2+(y−b)2=r.
1(x^2 + 2x) + 1(y^2 + 6y) = 61(x2+2x)+1(y2+6y)=6
1(x^2 + 2x + 1 - 1) + 1(y^2 + 6y + 9 - 9) = 61(x2+2x+1−1)+1(y2+6y+9−9)=6
1(x^2 + 2x + 1) - 1 + 1(y^2 + 6y + 9) - 9 = 61(x2+2x+1)−1+1(y2+6y+9)−9=6
(x + 1)^2 + (y + 3)^2 - 10 = 6(x+1)2+(y+3)2−10=6
(x + 1)^2 + (y + 3)^2 = 16(x+1)2+(y+3)2=16
In the form (x - a)^2 + (y - b)^2 = r(x−a)2+(y−b)2=r, the radius is given by sqrt(r)√r and the centre is at (a, b)(a,b). Then, the centre is at (-1, -3)(−1,−3) and the radius measures 44 units.
Hopefully this helps!
