If the straight line $ax + by + c = 0$ always passes through $(1, -2),$ then $a, b, c$ are

$A$ man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is $\frac{1}{4}$. Three stones $A, B$ and $C$ are placed at the points $(1,1), (2,2)$ and $(4,4)$ respectively. Which of these stones is/are on the path of the man?

Find the equation of the line perpendicular to the line $x-7y+5=0$ and having $x$-intercept $3$.

The equation of the line which makes a right-angled triangle with the axes whose area is $6$ sq. units and whose hypotenuse is $5$ units,is

Two lines $L_1$ and $L_2$ passing through the point $P(1, 2)$ cut the line $x+y=4$ at a distance of $\frac{\sqrt{6}}{3}$ units from $P$. Then the angles made by $L_1$ and $L_2$ with the positive $X$-axis are

Find the equation of the line,which makes intercepts $-3$ and $2$ on the $x$- and $y$-axes respectively.