If the points $A(5, k)$,$B(-3, 1)$ and $C(-7, -2)$ are collinear,then $k=$

The system of linear equations $ax - y + 2 = 0$ and $x + ay + 3 = 0$ has a unique solution. Then,the set of values of $a$ is . . . . . . .

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.

The $y$-intercept made by the line $x \cos \alpha + y \sin \alpha = a$ is:

The equation of the line passing through $(c, d)$ and parallel to $ax + by + c = 0$ is

The parallelism condition for two straight lines,one of which is specified by the equation $ax + by + c = 0$ and the other being represented parametrically by $x = \alpha t + \beta$ and $y = \gamma t + \delta$,is given by: