The lines $x-2 y+1=0,2 x-3 y-1=0$ and $3 x-y+k=0$ are concurrent. The angle between the lines $3 x-y+k=0$ and $m x-3 y+6=0$ is $45^{\circ}$. If $m$ is an integer, then $m-k=$

If $\tan ^{-1}(2 \sqrt{10})$ is the angle between the lines $a x^2+4 x y-2 y^2=0$ and $a \in Z$, then the product of the slopes of given lines is

The point $P(\alpha, \beta)(\alpha>0, \beta>0)$ undergoes the following transformations successively.

(a) Translation to a distance of 3 units in positive direction of $X$-axis.

(b) Reflection about the line $y=-x$.

(c) Rotation of axes through an angle of $\frac{\pi}{4}$ about the origin in the positive direction.

If the final position of that point $P$ is $(-4 \sqrt{2},-2 \sqrt{2})$, then $(\alpha+\beta)=$

If the line passing through the point $(4,-3)$ and having negative slope makes an angle of $45^{\circ}$ with the line joining the points $(1,1),(2,3)$, then the sum of intercepts of that line is