The perpendicular distance of the straight line $12x + 5y = 7$ from the origin is equal to

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

If $12a + 5b = 9$,where $a, b \in \mathbb{R}$,then the minimum value of $a^2 + b^2$ is:

Find the length of the perpendicular drawn from the origin to the line $\frac{x}{a} + \frac{y}{b} = 1$.

If the length of the perpendicular from the origin to the line $x/a + y/b = 1$ is $p$,then which of the following is true for $a^2, 4p^2, b^2$?

The vertices of a triangle are $A(-1, 3)$,$B(-2, 2)$,and $C(3, -1)$. $A$ new triangle is formed by shifting the sides of the triangle by one unit inwards. Then the equation of the side of the new triangle nearest to the origin is: