The line $x+2 y=k$ meets the curve $2 x^2-2 x y+3 y^2+2 x-y-1=0$ at two points $A$ and $B$. Let $O$ be the origin. If the line segments $O A$ and $O B$ are perpendicular to each other, then $k=$

If a straight line $L$ passing through the point $(5,-3)$ is inclined at an angle of $60^{\circ}$ to the line $\sqrt{3} x+y-9=0$ and $L$ intersects $X$-axis, then the equation of $L$ is

Let $\alpha, \beta$ and $\gamma$ be three non-zero real constants and $a, b$ and $c$ be three arbitrary real numbers which satisfy $\alpha a+\beta b+\gamma c=0$. Then, the point of concurrence of the family of lines $a x+b y+c=0$ is

If the algebraic sum of the perpendicular distances from the points $(2,0),(0,2)$ and $(1,1)$ to a variable line is zero, then the variable line always passes through a fixed point. The coordinates of that point are