The radical centre of the circles ${x^2} + {y^2} – 16x + 60 = 0,\,{x^2} + {y^2} – 12x + 27 = 0,$ ${x^2} + {y^2} – 12y + 8 = 0$ is

The equation of the circle which passes through the point of intersection of circles ${x^2} + {y^2} – 8x – 2y + 7 = 0$ and ${x^2} + {y^2} – 4x + 10y + 8 = 0$ and having its centre on $y$ – axis, will be

The equation of radical axis of the circles ${x^2} + {y^2} + x – y + 2 = 0$ and $3{x^2} + 3{y^2} – 4x – 12 = 0,$ is

The two circles ${x^2} + {y^2} – 2x + 22y + 5 = 0$ and ${x^2} + {y^2} + 14x + 6y + k = 0$ intersect orthogonally provided $k$ is equal to

Suppose we have two circles of radius 2 each in the plane such that the distance between their centers is $2 \sqrt{3}$. The area of the region common to both circles lies between