The distance between two parallel lines $3x + 4y - 8 = 0$ and $3x + 4y - 3 = 0$ is given by

The length of the perpendicular from the point $(a \cos \alpha, a \sin \alpha)$ to the line $y = x \tan \alpha + c, c > 0$ is .....

Statement $(A)$: The points $(2, 1)$ and $(-3, 5)$ lie on opposite sides of the line $3x - 2y + 1 = 0$.
Reason $(R)$: The algebraic perpendicular distances from the given points to the line have opposite signs.

Let two points be $A(1, -1)$ and $B(0, 2)$. If a point $P(x', y')$ is such that the area of $\Delta PAB = 5 \; \text{sq units}$ and it lies on the line $3x + y - 4\lambda = 0$,then a value of $\lambda$ is

If a line $l$ passes through $(k, 2k), (3k, 3k)$ and $(3, 1)$,where $k \neq 0$,then the distance from the origin to the line $l$ is

Given the lines $y + 2x = 3$ and $y + 2x = 5$ cut the axes at $A, B$ and $C, D$ respectively.
Statement-$1$ : $ABDC$ forms a quadrilateral and the point $(2, 3)$ lies inside the quadrilateral.
Statement-$2$ : The point $(2, 3)$ lies between the two parallel lines.