The equation of the circle which cuts all the three circles $4(x-1)^2+4(y-1)^2=1,4(x+1)^2+4(y-1)^2$ and $4(x+1)^2+4(y+1)^2=1$ orthogonally is

$A(a, 0)$ is a fixed point and $\theta$ is a parameter such that $0<\theta<2 \pi$. If $P(a \cos \theta, a \sin \theta)$ is a point on the circle $x^2+y^2=a^2$ and $Q(b \sin \theta,-b \cos \theta)$ is a point on the circle $x^2+y^2=b^2$, then the locus of the centroid of the $\triangle A P Q$ is

If the equation of the circle passing through the point $(8,8)$ and having the lines $x+2 y-2=0$ and $2 x+3 y-1=0$ as its diameters is $x^2+y^2+p x+q y+r=0$, then $p^2+q^2+r=$

If $2 x-3 y+1=0$ is the equation of the polar of a point $P\left(x_1, y_1\right)$ with respect to the circle $x^2+y^2-2 x+4 y+3=0$, then $3 x_1-y_1=$