The distance of point $(-2, 3)$ from the line $x - y - 5 = 0$ is

If two distinct points lying on the line $x+y=4$ are at a unit distance from the line $4x+3y-10=0$,and the distance between these two points is $d$,then the value of $d$ is:

Let $d$ be the distance between the parallel lines $3x - 2y + 5 = 0$ and $3x - 2y + 5 + 2\sqrt{13} = 0$. Let $L_1 \equiv 3x - 2y + k_1 = 0$ $(k_1 > 0)$ and $L_2 \equiv 3x - 2y + k_2 = 0$ $(k_2 > 0)$ be two lines that are at a distance of $\frac{4d}{\sqrt{13}}$ and $\frac{3d}{\sqrt{13}}$ from the line $3x - 2y + 5 = 0$,respectively. Then the combined equation of the lines $L_1 = 0$ and $L_2 = 0$ is:

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

If $2p$ is the length of the perpendicular from the origin to the line $\frac{x}{a} + \frac{y}{b} = 1$,then:

If $(\lambda^2, \lambda+1), \lambda \in \mathbb{Z}$ belongs to the region between the lines $x+2y-5=0$ and $3x-y+1=0$ which includes the origin,then the possible number of such points is