$A$ value of $k$ such that the straight lines $y-3kx+4=0$ and $(2k-1)x-(8k-1)y-6=0$ are perpendicular is

The equations of the lines passing through the point $(3,2)$ and making an acute angle of $45^{\circ}$ with the line $x-2y-3=0$ are

Let the angle between the lines $x-2y+3=0$ and $kx-y+2=0$ be $45^{\circ}$. If $k_1, k_2$ $(k_1 > k_2)$ are two distinct real values of $k$,then $k_1-2=$

The angle between the lines $2x - y + 5 = 0$ and $3x + y + 4 = 0$ is ...$^o$.

The equation of one of the straight lines which passes through the point $(1, 3)$ and makes an angle of $\tan^{-1}(\sqrt{2})$ with the straight line $y + 1 = 3\sqrt{2}x$ is:

If $\alpha, \beta$ $(\alpha > \beta)$ are two values of $k$ such that the equations $2x + (3 - 2k)y + (2k + 1) = 0$ and $kx + (k - 1)y - 4 = 0$ represent two perpendicular lines,then $\alpha^2 + 2\beta =$