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
${x^2} + {y^2} + 2x - 4y - 4 = 0$
${x^2} + {y^2} + 4x - 2y - 4 = 0$
${x^2} + {y^2} - 3x - 4y = 0$
${x^2} + {y^2} - 4x - 2y = 0$
The number of common tangents to the circles ${x^2} + {y^2} = 4$ and ${x^2} + {y^2} - 6x - 8y = 24$ is
The circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$ bisects the circumference of the circle ${x^2} + {y^2} + 2g'x + 2f'y + c' = 0$, if
For the two circles $x^2 + y^2 = 16$ and $x^2 + y^2 -2y = 0,$ there is/are
If a variable line, $3x + 4y -\lambda = 0$ is such that the two circles $x^2 + y^2 -2x -2y + 1 = 0$ and $x^2 + y^2 -18x -2y + 78 = 0$ are on its opposite sides, then the set of all values of $\lambda $ is the interval
The radical axis of the pair of circle ${x^2} + {y^2} = 144$ and ${x^2} + {y^2} - 15x + 12y = 0$ is