If the coordinates of the point of contact of the circles $x^2+y^2-4x+8y+4=0$ and $x^2+y^2+2x=0$ are $(a, b)$,then $a+2b=$

The slope of one of the direct common tangents drawn to the circles $x^2+y^2-2x+4y+1=0$ and $x^2+y^2-4x-2y+4=0$ is

The circles $x^2+y^2+2ax+c=0$ and $x^2+y^2+2by+c=0$ touch each other externally,if

If $C_1$ and $C_2$ are the centres of similitude with respect to the circles $x^2+y^2-14 x+6 y+33=0$ and $x^2+y^2+30 x-2 y+1=0$,then the equation of the circle with $C_1 C_2$ as diameter is

The condition for the coaxial system $x^2+y^2+2 \lambda x+c=0$,where $\lambda$ is a parameter and $c$ is a constant,to have distinct limiting points,is

If the length of the transverse common tangent to the circles $x^{2} + y^{2} = 1$ and $(x - h)^{2} + y^{2} = 1$ is $2\sqrt{3}$,find the value of $h$.