On which side of the line $7x + 5y - 9 = 0$ do the points $(3, 4)$ and $(-9, 6)$ lie?

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:

The number of points on the line $x+y=4$ which are at a unit distance from the line $2x+2y=5$ is

The system of equations $x + y = 2$ and $2x + 2y = 3$ will have:

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

Lines are drawn parallel to the line $4x - 3y + 2 = 0$ at a distance of $\frac{3}{5}$ from the origin. Which one of the following points lies on any of these lines?