The minimum area of the triangle formed by the variable line $3 \cos \theta \cdot x + 4 \sin \theta \cdot y = 12$ and the coordinate axes is

If the equations $y = mx + c$ and $x \cos \alpha + y \sin \alpha = p$ represent the same straight line,then:

The lines $2x + 3y = 6$ and $2x + 3y = 8$ cut the $X$-axis at $A$ and $B$,respectively. $A$ line $L$ drawn through the point $(2, 2)$ meets the $X$-axis at $C$ in such a way that the abscissae of $A, B,$ and $C$ are in arithmetic progression. Then,the equation of the line $L$ is

Find the equation of the line passing through the point $(4, 3)$ such that the sum of its intercepts on the axes is $-1$.

The line joining two points $A(2, 0)$ and $B(3, 1)$ is rotated about $A$ in the anticlockwise direction through an angle of $15^{\circ}$. The equation of the line in the new position is:

$A$ line is passing through the point $(4,3)$ and the sum of its intercepts made on the coordinate axes is $14$. Then an equation of that line is