If the pair of lines $3 x^2-5 x y+\mathrm{p} y^2=0$ and $6 x^2-x y-5 y^2=0$ have one line common, then $\mathrm{p}=$

The line MN whose equation is $x-y-2=0$ cuts the X -axis at M and co-ordinates of N are $(4,2)$. The line MN is rotated about M through $45^{\circ}$ in anticlockwise direction. The equation of the line MN in the new position is

The circumcenter of the triangle formed by lines $x y+2 x+2 y+4=0$ and $x+y+2=0$ is

The slopes of the lines represented by $6 x^2+2 \mathrm{hxy}+y^2=0$ are in the ratio $2: 3$, then $\mathrm{h}=$