If a unit circle $S \equiv x^2+y^2+2gx+2fy+c=0$ touches the circle $S^{\prime} \equiv x^2+y^2-6x+6y+2=0$ externally at the point $P(-1, -3)$,then $g+f+c=$

If the circles $x^2+y^2=9$ and $x^2+y^2+2\alpha x+2y+1=0$ touch each other internally,then the value of $\alpha^3$ is

The figure shows $\Delta ABC$ with $AB = 3, AC = 4$ and $BC = 5$. Three circles $S_1, S_2$ and $S_3$ have their centers at $A, B$ and $C$ respectively and they touch each other externally. The sum of the areas of the three circles is: (in $\pi$)

If $(1, a)$ and $(b, 2)$ are conjugate points with respect to the circle $x^2+y^2=25$,then $4a+2b=$

The number of circles that touch all the three lines $x+y-1=0$,$x-y-1=0$,and $y+1=0$ is

Let the tangents drawn from $P(-1, -1)$ to the circle $x^2 + y^2 - 2x - 4y - 4 = 0$ touch the circle at the points $A$ and $B$. Then the area of the triangle $PAB$ (in square units) is