The polars of $(-1, 2)$ with respect to the two circles $S_1 \equiv x^2+y^2+6y+7=0$ and $S_2 \equiv x^2+y^2+6x+1=0$ are

For all real values of $k$,the polar of the point $(2k, k-4)$ with respect to the circle $x^2+y^2-4x-6y+1=0$ passes through the point:

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 pole of the line $\frac{x}{a} + \frac{y}{b} = 1$ with respect to the circle $x^2 + y^2 = c^2$ is

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:

Consider the following statements:
$I$. If $P(x_1, y_1)$ and $Q(x_2, y_2)$ are conjugate points with respect to the circle $x^2+y^2+2gx+2fy+c=0$,then $x_1x_2+y_1y_2+g(x_1+x_2)+f(y_1+y_2)+c=0$.
$II$. The pole of the line $x+y+1=0$ with respect to the circle $x^2+y^2=9$ is $(9, 9)$.
Which of the following is true?