Question

The length of the perpendicular from the origin to a line is 7 and the line makes an angle of 150° with the positive direction of Y-axis. Find the equation of the line.

Answer 1

Let AB be the given line which make an angle of 150⁰ with the positive
direction of y-axis and OQ be the perpendicular drawn from the origin on the line.
Here, p = 7 and $\mathrm{\alpha }={30}^{\circ }$

So, the equation of the line AB is

$$\begin{gathered} x\mathrm{cos\alpha }+y\mathrm{sin\alpha }=p \\ \Rightarrow x\cos {30}^{\circ }+y\sin 30°=7 \\ \Rightarrow \frac{\sqrt{3}x}{2}+\frac{y}{2}=7 \\ \Rightarrow \sqrt{3}x+y=14 \end{gathered}$$