Question

Find the equation of a line perpendicular to the line \[\sqrt{3}x - y + 5 = 0\] and at a distance of 3 units from the origin.

Answer 1

The line perpendicular to \[\sqrt{3}x - y + 5 = 0\] is \[x + \sqrt{3}y + \lambda = 0\]

It is given that the line \[x + \sqrt{3}y + \lambda = 0\] is at a distance of 3 units from the origin.

\[\therefore \left| \frac{\lambda}{\sqrt{1 + 3}} \right| = 3\]

\[ \Rightarrow \lambda = \pm 6\]

Substituting the value of \[\lambda\] we get \[x + \sqrt{3}y \pm 6 = 0\] ,which is  equation of the required line.