If the point $(5, 2)$ divides the segment of the line between the axes into two equal parts,then its equation is:

The sum of the squares of the intercepts made by the line $5x - 2y = 10$ on the coordinate axes equals:

$A$ line passes through the point $(1, 2)$ and makes an angle of $60^{\circ}$ with the $x$-axis. The coordinates of the points on this line at a distance of $3$ units from the point $(1, 2)$ are:

If the line $\frac{x}{a} + \frac{y}{b} = 1$ passes through the points $(2, -3)$ and $(4, -5)$,then $(a, b) = $

$A$ 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 equation of the line passing through $(5, 3)$ and perpendicular to $2x + y - 7 = 0$ is