Straight Line Question 345

Question: The equations of the lines through the origin making an angle of $ 60^{o} $ with the line $ x+y\sqrt{3}+3\sqrt{3}=0 $ are

Options:

A) $ y=0,\ x-y\sqrt{3}=0 $

B) $ x=0,\ x-y\sqrt{3}=0 $

C) $ x=0,\ x+y\sqrt{3}=0 $

D) $ y=0,\ x+y\sqrt{3}=0 $

Show Answer

Answer:

Correct Answer: B

Solution:

  • Since the line $ x+y\sqrt{3}+3\sqrt{3}=0 $ makes an angle of $ 150^{o} $ with $ x $ -axis. Therefore, the required lines will make angles of $ 90^{o} $ and $ 210^{o} $ i.e., $ 30^{o} $ with the positive direction of x-axis. Hence the lines are $ x=0 $ and $ y=\frac{1}{\sqrt{3}}x $ .