When the origin is shifted to the point $\left(\frac{3}{2}, \frac{3}{2}\right)$ by the translation of coordinate axes, then the transformed equation of $32 x^2+8 x y+32 y^2-108 x-108 y+99=0$ is

A line $L_1$ passing through $A(3,4)$ and having slope 1 cuts another line $L_2$ passing through $C$ at $B$, such that $A B=A C$. If the equation of line $B C$ is $2 x-y+4=0$, then the equation of $A C$ is

Angles made with the $X$-axis by the two lines passing through the point $P(1,2)$ and cutting the line $x+y=4$ at a distance $\frac{\sqrt{6}}{3}$ units from the point $P$ are

The straight lines $x+3 y-9=0,4 x+5 y-1=0$, $p x+q y+10=0$ are concurrent, if the line $5 x+6 y+10=0$ passes through the point