The equation of the circle which passes through the points of intersection of the circles $${x^2} + {y^2} - 6x = 0$$ and $${x^2} + {y^2} - 6y = 0$$, and has its centre at $$\left( {{3 \over 2},{3 \over 2}} \right)$$ is

The equation $$(x - {x_1})(x - {x_2}) + (y - {y_1})(y - {y_2}) = 0$$ represents a circle whose centre is

The circles $${x^2} + {y^2} + 6x + 6y = 0$$ and $${x^2} + {y^2} - 12x - 12y = 0$$

The locus of the centres of the circles which touch both the axes is given by