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Find the centre and Radius of x2 + y2 + 6y = 0
1. (0, 3), 3
2. (-3, 0), 3
3. (3, 0), 3
4. (0, -3), 3
5. None of these

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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

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