If the point $(a, 2a)$ lies between the lines $|x + y + 1| = 4$,then the complete set of values of $'a'$ is:

$A$ rectangle is formed by the lines $x=0, x=3, y=0$ and $y=4$. Let the line $L$ be perpendicular to $3x+y+6=0$ and divide the area of the rectangle into two equal parts. Then the distance of the point $(\frac{1}{2}, -5)$ from the line $L$ is equal to:

The equations of the lines passing through the point $(1, 0)$ and at a distance $\frac{\sqrt{3}}{2}$ from the origin are:

The positions of the points $(3, 4)$ and $(2, -6)$ with respect to the line $3x - 4y = 8$ are:

Identify the point on the line $2x + 3y + 7 = 0$,which is at a distance of $3$ units from $(1, -3)$.

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: