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 $\mathrm{h}=$

The straight line passing through $(-3,6)$ and midpoint of the line segment joining the points $(4,-5)$ and ( $-2,9$ ) have inclination