From a point $(1,0)$ on the circle $x^2+y^2-2x+2y+1=0$,if chords are drawn to this circle,then the locus of the poles of these chords with respect to the circle $x^2+y^2=4$ is:

If the inverse point of the point $(-1, 1)$ with respect to the circle $x^2+y^2-2x+2y-1=0$ is $(p, q)$,then $p^2+q^2=$

The polar of $(1, -2)$ with respect to $x^2+y^2-10x-10y+25=0$ is

The inverse of the point $(1, 2)$ with respect to the circle $x^2 + y^2 - 4x - 6y + 9 = 0$ is

The point of concurrence of all conjugate lines of the line $5x + 7y - 78 = 0$ with respect to the circle $x^2 + y^2 + 6x + 8y - 96 = 0$ is

The normal to a circle $S=0$ at $P(1,3)$ is $x+2y=7$ and it has another normal at $Q(3,5)$ which is the polar of the point $A(7, -1/2)$ with respect to the circle $x^2+y^2-4x+6y-12=0$. Then,the equation of the circle $S=0$ is