Straight Line Question 324

Question: Equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of $ 120^{o} $ with the x?axis, is [MNR 1986]

Options:

A) $ x\sqrt{3}+y+8=0 $

B) $ x\sqrt{3}-y=8 $

C) $ x\sqrt{3}-y=8 $

D) $ x-\sqrt{3}\ y+8=0 $

Show Answer

Answer:

Correct Answer: A

Solution:

  • Slope $ =-\sqrt{3} $

$ \therefore $ Line is $ y=-\sqrt{3}x+c $ Þ $ \sqrt{3}x+y=c $ Now $ \frac{c}{2}=|4|\Rightarrow c=\pm 8\Rightarrow x\sqrt{3}+y=\pm 8 $ .