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 \[\alpha = {30}^\circ\]

So, the equation of the line AB  is

\[xcos\alpha + ysin\alpha = p \]

\[ \Rightarrow x \text {cos} {30}^\circ + y \text { sin }30^\circ = 7\]

\[ \Rightarrow \frac{\sqrt{3}x}{2} + \frac{y}{2} = 7\]

\[ \Rightarrow \sqrt{3}x + y = 14\]