The equation of the line perpendicular to $x = c$ is

Find the equation of the line which is at a perpendicular distance of $5$ units from the origin and the angle made by the perpendicular with the positive $x-$ axis is $30^{\circ}$.

Find the equation of the line perpendicular to the line $2x - 3y = 5$ and passing through the point $(1, -1)$.

Find the $y$-intercept of a line that is perpendicular to $3x + y = 3$ and passes through the point $(2, 2)$.

The points $A(-a, -b)$,$B(0, 0)$,$C(a, b)$,and $D(a^2, ab)$ are

The equation of a line passing through $(p \cos \alpha, p \sin \alpha)$ and making an angle $(90^\circ + \alpha)$ with the positive direction of the $X$-axis is: