The equations of the diagonals of the square formed by the lines $x = 0,$ $y = 0,$ $x = 1,$ and $y = 1$ are

The number of lines passing through $A(3, 4)$ such that the sum of their non-zero intercepts is zero is:

$\beta$ is the angle made by the perpendicular drawn from the origin to the line $L \equiv x+y-2=0$ with the positive $X$-axis in the anticlockwise direction. If '$a$' is the $X$-intercept of the line $L=0$ and $p$ is the perpendicular distance from the origin to the line $L=0$,then $a \tan \beta + p^2 =$

Let $PS$ be the median of the triangle with vertices $P(2, 2)$,$Q(6, -1)$,and $R(7, 3)$. The equation of the line passing through $(1, -1)$ and parallel to $PS$ is

Consider the equation $y - y_1 = m(x - x_1)$. If $m$ and $x_1$ are fixed and different lines are drawn for different values of $y_1$,then:

The length of the perpendicular from the origin to a line is $9$ and the perpendicular makes an angle of $120^{\circ}$ with the positive direction of the $y$-axis. Find the equation of the line.