The equation of the circle passing through the point $(-2, 4)$ and through the points of intersection of the circle ${x^2} + {y^2} - 2x - 6y + 6 = 0$ and the line $3x + 2y - 5 = 0$, is
${x^2} + {y^2} + 2x - 4y - 4 = 0$
${x^2} + {y^2} + 4x - 2y - 4 = 0$
${x^2} + {y^2} - 3x - 4y = 0$
${x^2} + {y^2} - 4x - 2y = 0$
If a circle passes through the point $(a , b) \&$ cuts the circle $x^2 + y^2= K^2$ orthogonally, then the equation of the locus of its centre is :
If the centre of a circle which passing through the points of intersection of the circles ${x^2} + {y^2} - 6x + 2y + 4 = 0$and ${x^2} + {y^2} + 2x - 4y - 6 = 0$ is on the line $y = x$, then the equation of the circle is
The gradient of the radical axis of the circles ${x^2} + {y^2} - 3x - 4y + 5 = 0$ and $3{x^2} + 3{y^2} - 7x + 8y + 11 = 0$ is
The radical axis of the pair of circle ${x^2} + {y^2} = 144$ and ${x^2} + {y^2} - 15x + 12y = 0$ is
The two circles ${x^2} + {y^2} - 4y = 0$ and ${x^2} + {y^2} - 8y = 0$