The point of concurrence of all the chords of the curve $3 x^2-y^2-2 x+4 y=0$ which subtend a right angle at the origin is

Let $d$ be the distance between the parallel lines $3 x-2 y+5=0$ and $3 x-2 y+5+2 \sqrt{13}=0$.

Let $L_1 \equiv 3 x-2 y+k_1=0\left(k_1>0\right)$ and $L_2 \equiv 3 x-2 y+k_2=0\left(k_2>0\right)$ be two lines that are at the distance of $\frac{4 d}{\sqrt{13}}$ and $\frac{3 d}{\sqrt{13}}$ from the line $3 x-2 y+5=0$.

Then, the combined equation of the lines $L_1=0$ and $L_2=0$ is

If $(h, k)$ is the image of the point $(3,-4)$ with respect to the line $2 x-3 y-5=0$ and $(l, m)$ is the foot of the perpendicular from $(h, k)$ on to the line $3 x+2 y+12=0$, then $l h+m k+1=$

A straight line parallel to the line $y=\sqrt{3} x$ passes through $Q(2,3)$ and cuts the line $2 x+4 y-27=0$ at $P$. Then, the length of the line segment $P Q$ is