Correct Answer - Option 4 : (0, -3), 3
Concept:
Standard equation of the circle with radius r and centre (h, k) is given by:
\({\left( {x - h} \right)^2} + {\left( {y - k} \right)^2} = {r^2}\)
Calculation:
\({x^2} + {y^2} + 6y = 0\)
\({x^2} + {y^2} + 6y + 9 - 9 = {x^2} + {\left( {y + 3} \right)^2} - 9 = 0\)
\({x^2} + {\left( {y + 3} \right)^2} = 9\)
Standard equation of the circle with radius r and centre (h, k) is given by:
\({\left( {x - h} \right)^2} + {\left( {y - k} \right)^2} = {r^2}\)
By comparing: Here h = 0, k = -3, r = 3
Centre: (0, -3), Radius: 3