If the slope of a line is $2$ and it makes an intercept of $-4$ on the $y$-axis,then its equation is:

The equation of the line,where the length of the perpendicular segment from the origin to the line is $4$ and the inclination of this perpendicular segment with the positive direction of the $X$-axis is $30^{\circ}$,is:

What is the equation of the line passing through $(-1, 1)$ and perpendicular to the line $2x + 3y + 4 = 0$?

If $\alpha$ is the angle made by the perpendicular drawn from the origin to the line $12x - 5y + 13 = 0$ with the positive $X$-axis in the anti-clockwise direction,then $\alpha =$

$A$ 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?

The ends of the base of an isosceles triangle are at $(2a, 0)$ and $(0, a)$. The equation of one side is $x = 2a$. The equation of the other side is