If the two lines $7x + 3y + 9 = 0$ and $y = kx + 7$ are perpendicular to each other,find the value of $k$.

The distance of a point $(2, 5)$ from the line $3x + y + 4 = 0$ measured along the lines $L_1$ and $L_2$ are the same. If the slope of line $L_1$ is $\frac{3}{4}$,then the slope of the line $L_2$ is

The slope of a line $L$ is $2$. If $m_1$ and $m_2$ are the slopes of two lines which are inclined at an angle of $\frac{\pi}{6}$ with $L$,then $m_1 + m_2 =$

The lines $y = 2x$ and $x = -2y$ are

If two lines $x+(a-1)y=1$ and $2x+a^2y=1$ $(a \in R-\{0,1\})$ are perpendicular,then the distance of their point of intersection from the origin is

The value of $k (> 0)$,such that the angle between the lines $4x - y + 7 = 0$ and $kx - 5y - 9 = 0$ is $45^{\circ}$,is