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 ${x^2} + {y^2} - 2x + 6y + 6 = 0$ and ${x^2} + {y^2} - 5x + 6y + 15 = 0$ touch each other. The equation of their common tangent is

The minimum distance between any two points $P _{1}$ and $P _{2}$ while considering point $P _{1}$ on one circle and point $P _{2}$ on the other circle for the given circles' equations

$x^{2}+y^{2}-10 x-10 y+41=0$

$x^{2}+y^{2}-24 x-10 y+160=0$ is .........

Let the equation $x^{2}+y^{2}+p x+(1-p) y+5=0$ represent circles of varying radius $\mathrm{r} \in(0,5]$. Then the number of elements in the set $S=\left\{q: q=p^{2}\right.$ and $\mathrm{q}$ is an integer $\}$ is ..... .

The number of common tangents to the circles ${x^2} + {y^2} - 4x - 6y - 12 = 0$ and ${x^2} + {y^2} + 6x + 18y + 26 = 0$ is

The number of common tangents to the circles ${x^2} + {y^2} = 1$and ${x^2} + {y^2} - 4x + 3 = 0$ is