Question

Find the equation of the line on which the length of the perpendicular segment from the origin to the line is 4 and the inclination of the perpendicular segment with the positive direction of x-axis is 30°.

Answer 1

Given:p = 4 and ω = 30°.
Equation of the line in normal form is

\[x \cos \omega + y \sin \omega = p\]

\[ \Rightarrow x \cos \left( {30}^\circ\right) + y \sin \left( {30}^\circ \right) = 4\]

\[ \Rightarrow x\frac{\sqrt{3}}{2} + y\frac{1}{2} = 4\]

\[ \Rightarrow \sqrt{3}x + y = 8\]

Hence, the equation of the line is \[\sqrt{3}x + y = 8\].