If the points $(2,3)$ and $(K,-2)$ are conjugate with respect to the circle $x^2+y^2-2x+4y-2=0$,then $K=$

If the polar of a point on the circle $x^2+y^2=p^2$ with respect to the circle $x^2+y^2=q^2$ touches the circle $x^2+y^2=r^2$,then $p, q, r$ are in

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 $5x + 6y - 34 = 0$ and $2x + y + c = 0$ are conjugate lines with respect to the circle $x^2 + y^2 - 8x - 10y + 25 = 0$,then which of the following points lies on the line $2x + y + c = 0$?

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

The lines $x \cos \alpha + y \sin \alpha = P, \alpha \in R$ are chords of the hyperbola $\frac{x^2}{9} - \frac{y^2}{36} = 1$ and they subtend a right angle at the centre of the hyperbola. The locus of the poles of these lines with respect to the given hyperbola is