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

Find the value of $k$ for which the line $(k-3) x - (4-k^2) y + k^2 - 7k + 6 = 0$ passes through the origin.

The equation of a straight line,where the length of the perpendicular from the origin is $4$ units and the line makes an angle of $120^{\circ}$ with the $x$-axis,is:

Find the equation of the line passing through the point $(2, 3)$ and perpendicular to the line joining the points $(-5, 6)$ and $(-6, 5)$.

The angles made with the $X$-axis by the two lines passing through the point $P(1, 2)$ and cutting the line $x+y=4$ at a distance $\frac{\sqrt{6}}{3}$ units from the point $P$ are

The $y$-intercept of the line passing through $A(6, 1)$ and perpendicular to the line $x - 2y = 4$ is: