If the perpendicular distance from the point $(1, 1)$ to the line $3x + 4y + c = 0$ is $7$,then the possible values of $c$ are:

If a line $L$ is perpendicular to the line $5x - y = 1$,and the area of the triangle formed by the line $L$ and the coordinate axes is $5$,then the distance of line $L$ from the line $x + 5y = 0$ is

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

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 $L_2$.

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

If the point $(1, a)$ lies between the lines $x + y = 1$ and $2(x + y) = 3$,then in which interval does $a$ lie?