Find the distance between the lines $3x + 2y + 7 = 0$ and $6x + 4y + 3 = 0$.

Let $A(a, b)$,$B(3, 4)$,and $C(-6, -8)$ respectively denote the centroid,circumcentre,and orthocentre of a triangle. Then,the distance of the point $P(2a+3, 7b+5)$ from the line $2x+3y-4=0$ measured parallel to the line $x-2y-1=0$ is

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

Let the equation $x(x+2)(12-k)=2$ have equal roots. Then the distance of the point $(k, \frac{k}{2})$ from the line $3x+4y+5=0$ is

On which side of the line $3x - 4y + 5 = 0$ does the point $(3, -4)$ lie?

The line $L$ given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line $K$ is parallel to $L$ and has the equation $\frac{x}{c}+\frac{y}{3}=1$. Then the distance between $L$ and $K$ is