Question

Find the equation of a line for p = 4, α = 150°.

Answer 1

 Here, p = 4, α = 150°
So, the equation of the line in normal form is

\[x\cos {150}^\circ + y\sin {150}^\circ = 4\]

\[ \Rightarrow x\cos\left( 180^\circ - {30}^\circ \right) + y\sin\left( 180^\circ - {30}^\circ \right) = 4\]

\[ \Rightarrow - x\cos {30}^\circ + y\sin {30}^\circ = 4\]

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

\[ \Rightarrow \sqrt{3}x - y + 8 = 0\]