If $(4,2)$ and $(k,-3)$ are conjugate points with respect to $x^2+y^2-5x+8y+6=0$,then $k$ equals

If the polar of a circle $x^2 + y^2 = a^2$ with respect to a point $(x', y')$ is $Ax + By + C = 0$,then its pole will be:

The locus of the poles of normal chords of an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is given by:

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?

If $2x - 3y + 3 = 0$ and $x + 2y + k = 0$ are conjugate lines with respect to the circle $S \equiv x^2 + y^2 + 8x - 6y - 24 = 0$,then the length of the tangent drawn from the point $\left(\frac{k}{4}, \frac{k}{3}\right)$ to the circle $S = 0$ is

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