$(a, b)$ is the point of concurrency of the lines $x-3 y+3=0, k x+y+k=0$ and $2 x+y-8=0$. If the perpendicular distance from the origin to the line $L=a x-b y+2 k=0$ is $p$, then the perpendicular distance from the point $(2,3)$ to $L=0$ is

If $(4,3)$ and $(1,-2)$ are the end points of a diagonal of a square, then the equation of one of its sides is

Area of the triangle bounded by the lines given by the equations $12 x^2-20 x y+7 y^2=0$ and $x+y-1=0$ is

The angle, by which the coordinate axes are to be rotated about the origin so that the transformed equation of $\sqrt{3} x^2+(\sqrt{3}-1) x y-y^2=0$ would be free from $x y$-term is