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

Two points $P(a, 2)$ and $Q(1, b)$ lie on either side of the line $2x - 3y + 1 = 0$. If $P$ is the point of intersection of the lines $4x + 3y + k = 0$ and $3x + 4y + k = 0$,then the range of $b$ is

Let the centroid of an equilateral triangle $ABC$ be at the origin. Let one of the sides of the equilateral triangle be along the straight line $x + y = 3$. If $R$ and $r$ are the radius of the circumcircle and incircle respectively of $\Delta ABC$,then $(R + r)$ is equal to ..... .

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

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

Let the line $L$ drawn perpendicular to the lines $2x - 3y + 4 = 0$ and $6x - 9y + 7 = 0$ meet them at $A$ and $B$ respectively. If $P(1, 1)$ is a point on $L$,then the ratio in which $P$ divides $AB$ is