The opposite vertices of a square are $(1, 2)$ and $(3, 8)$. Then,the equation of the diagonal of the square passing through the point $(1, 2)$ is:

$A$ line $L$ perpendicular to the line $5x - 12y + 6 = 0$ makes a positive intercept on the $Y$-axis. If the distance from the origin to the line $L$ is $2$ units and the angle made by the perpendicular drawn from the origin to the line $L$ with the positive $X$-axis is $\theta$,then $\tan \theta + \cot \theta =$

If the line $2x + 3y = 5$ and $y = mx + c$ are parallel,then:

The points $A(-a, -b)$,$B(0, 0)$,$C(a, b)$,and $D(a^2, ab)$ are

Find the angle in degrees $(^o)$ made by the line joining the points $(1, 0)$ and $(-2, \sqrt{3})$ with the $x$-axis.

$A$ 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?