The distance between the point $(2,1)$ and the image of the point $(3,-1)$ with respect to the line $2 x+y-1=0$ is

Let $O A B C$ be a parallelogram. The equation of one diagonal $A C$ is $x+y-1=0$ and the combined equation of the sides $O A, O C$ is $2 x^2-y^2=0$. If $G$ is centroid of the triangle $O A C$, then $B G=$

The acute angle between the pair of straight lines joining the origin to the points of intersection of the line $x+y-1=0$ with the pair of straight lines $k x^2+8 x y-3 y^2+2 x-4 y-1=0$ is

When the coordinate axes are rotated through an angle $\theta$ in anti clockwise direction, if the transformed equation of $x^2+y^2+2 x y+2 x+6 y+1=0$ is $(2+\sqrt{3}) X^2+2 X Y+(2-\sqrt{3}) Y^2+a X+b Y+2=0$, then $3 a-b=$