If $(a, 8)$ is a point on the line segment joining $(2, 5)$ and $(4, -1)$,then the value of $a$ is:

If $a, b$ are positive real numbers such that the lines $ax + 9y = 5$ and $4x + by = 3$ are parallel,then the least possible value of $a + b$ is

$A$ line passes through $(2,2)$ and is perpendicular to the line $3x+y=3$. Its $y$-intercept 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 $\tan \theta + \cot \theta =$

Find the equation of the line such that the perpendicular drawn from the origin to the line makes an angle of $30^{\circ}$ with the $x$-axis and the line forms a triangle of area $\frac{50}{\sqrt{3}}$ with the axes.

Find the equation of the straight line passing through the point $(3, 4)$ such that the sum of its intercepts on the axes is $14$.