If the points $(1, 2)$ and $(3, 4)$ lie on opposite sides of the line $3x - 5y + a = 0$,then:

The distance of the point $(2, 5)$ from the line $3x + y + 4 = 0$,measured parallel to the line $3x - 4y + 8 = 0$,is

The number of straight lines that can be drawn through the point $(-3, 4)$ which are at a distance of $5$ units from the point $(2, -8)$ is

The equations of the lines passing through the point of intersection of the lines $x - y + 1 = 0$ and $2x - 3y + 5 = 0$ and whose distance from the point $(3, 2)$ is $\frac{7}{5}$ are:

Find the distance between the parallel lines $l(x + y) + p = 0$ and $l(x + y) - r = 0$.

The angle made by a line $L$ with the positive $X$-axis measured in the positive direction is $\frac{\pi}{6}$ and the intercept made by $L$ on the $Y$-axis is negative. If $L$ is at a distance of $5$ units from the origin,then the perpendicular distance from the point $(1, -\sqrt{3})$ to the line $L$ is