The distance between the lines $3x + 4y = 9$ and $6x + 8y = 15$ is

Reduce the equation $x-\sqrt{3} y+8=0$ into normal form. Find the perpendicular distance from the origin and the angle between the perpendicular and the positive $x$-axis.

$A$ line $L_1$ passing through the point of intersection of the lines $x-2y+3=0$ and $2x-y=0$ is parallel to the line $L_2$. If $L_2$ passes through the origin and also through the point of intersection of the lines $3x-y+2=0$ and $x-3y-2=0$,then the distance between the lines $L_1$ and $L_2$ is

Let the line $L$ drawn perpendicular to the lines $2x - 3y + 4 = 0$ and $6x - 9y + 7 = 0$ meet them at $A$ and $B$ respectively. If $P(1, 1)$ is a point on $L$,then the ratio in which $P$ divides $AB$ is

If a point $(\alpha, \beta)$ on the line $3x + y = 0$ and the point $(3, 4)$ lie on opposite sides of the line $3x - 4y - 8 = 0$,then which of the following is correct?

Find the equation of the line which is equidistant from the parallel lines $9x + 6y - 7 = 0$ and $3x + 2y + 6 = 0$.