The pole of the straight line $x+4y=4$ with respect to the ellipse $x^2+4y^2=4$ is

The polar of a point with respect to the circle $x^2+y^2-10x+12y-3=0$,which is neither a tangent nor a chord of contact,is:

Let $S \equiv x^2+y^2-8x+10y+5=0$ be a circle. Let $P(1,1)$ and $Q(1,-1)$ be two points. Then the point of intersection of the polar of $P$ with respect to $S=0$ and the chord with $Q$ as mid-point to $S=0$ is

Consider the point $P(\alpha, \beta)$ on the line $2x+y=1$. If $P$ and $(3,2)$ are conjugate points with respect to the circle $x^2+y^2=4$,then $\alpha+\beta=$

If the polar of a point $P$ with respect to a circle of radius $r$ which touches the coordinate axes and lies in the first quadrant is $x+2y=4r$,then the point $P$ is

The pole of the straight line $9x + y - 28 = 0$ with respect to the circle $2x^2 + 2y^2 - 3x + 5y - 7 = 0$ is