Find the equation of a line passing through the point $(2, 5/3)$ such that the segment of the line intercepted between the axes is divided by the point in the ratio $5 : 4$.

Find the equation of the line which passes through $(2, 2\sqrt{3})$ and is inclined with the $x-$axis at an angle of $75^{\circ}$.

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:

If the coordinates of the points $A$ and $B$ are $(3, 3)$ and $(7, 6)$,then the length of the portion of the line $AB$ intercepted between the axes is

The area of the triangle formed by the line $L$ with the coordinate axes is $12$ sq. units. If $L$ passes through the point $(12, 4)$ and the product $P$ of the $X$-intercept of $L$ and the square of the $Y$-intercept of $L$ is negative,then $P=$

Find the equation of a line that makes an angle of $60^{\circ}$ with the $x$-axis and makes an intercept of $5$ units on the negative direction of the $y$-axis.