The image of every point lying on the curve $x^2+y^2=1$ in the line $x+y=1$ satisfies the equation

If the inverse of $P(-3,5)$ with respect to a circle is $(1,3)$ then polar of $P$ with respect to that circle is

If the tangent drawn at the point $P$ on the circle $x^2+y^2+6 x+6 y=2$ meets the straight line $5 x-2 y+6=0$ at a point $Q$ on the $Y$-axis, then the length of $P Q$ is

The line $4 x+3 y-4=0$ divides the circumference of a circle in the ratio $1: 2$. If $C(5,3)$ is the centre of that circle, then equation of the circle is