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

The equation of the line passing through $(a \cos^3 \theta, a \sin^3 \theta)$ and parallel to the line $x \sec \theta + y \csc \theta = a$ is:

The length of the perpendicular from the origin to a line is $4$ units,and the perpendicular makes an angle of $30^{\circ}$ with the positive direction of the $x$-axis. Find the equation of the line.

The equation of the line passing through $(5, 3)$ and perpendicular to $2x + y - 7 = 0$ is

Let a line intersect the co-ordinate axes in points $A$ and $B$ such that the area of the triangle $OAB$ is $12$ sq. units. If the line passes through the point $(2,3)$,then the equation of the line is

Find the equation of the line passing through the point $(2, -3)$ such that the sum of its intercepts on the axes is $-2$.