The distance between the two parallel lines $y = 2x + 7$ and $y = 2x + 5$ is:

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

If $p$ is the length of the perpendicular from the origin to the line whose intercepts on the axes are $a$ and $b$,then $\frac{1}{a^2}+\frac{1}{b^2}=$

$A$ straight line is parallel to the lines $3x - y - 3 = 0$ and $3x - y + 5 = 0$ and lies between them. If its distance from these lines is in the ratio $3 : 5$,then its equation is:

Let the origin be the centroid of an equilateral triangle $ABC$ and one of its sides be along the straight line $x+y=3$. If $R$ and $r$ are its circumradius and inradius respectively,then $R+r=$

The line $L_1$ given by $\frac{x}{p} + \frac{y}{2} = 1$ passes through the point $(5, 0)$. The line $L_2$ given by $\frac{x}{10} + \frac{y}{q} = 1$ is parallel to $L_1$. Find the distance between the lines $L_1$ and $L_2$.