If the line through the points $(-2, 6)$ and $(4, 8)$ is perpendicular to the line passing through the points $(8, 12)$ and $(x, 24)$,then the value of $x$ 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 $\alpha^2 + 2\beta =$

The equation of the straight line passing through the point $(3, 2)$ and inclined at an angle of $60^{\circ}$ with the line $\sqrt{3} x + y = 1$ is

The acute angle between the lines $x-3=0$ and $x+y=19$ is: (in $^{\circ}$)

If a straight line $L$ passing through the point $(5, -3)$ is inclined at an angle of $60^{\circ}$ to the line $\sqrt{3}x + y - 9 = 0$ and $L$ intersects the $X$-axis,then the equation of $L$ is

The angle between the straight lines $3x + 4y + 9 = 0$ and $x - 7y - 22 = 0$ is