Straight Line Question 241

Question: The length of the perpendicular from the origin to a line is 7 and line makes an angle of $ 150{}^\circ $ with the positive direction of y-axis, then the equation of the line is

Options:

A) $ \sqrt{3}x+y=7 $

B) $ \sqrt{3}x-y=14 $

C) $ \sqrt{3}x+y+14=0 $

D) $ \sqrt{3}x+y-14=0 $

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Answer:

Correct Answer: D

Solution:

  • [d] Here p=7 and $ \alpha =30{}^\circ $

$ \therefore $ Equation of the required line is $ x\cos 30{}^\circ +y\sin 30{}^\circ =7 $ or $ x\frac{\sqrt{3}}{2}+y\times \frac{1}{2}=7 $ or $ \sqrt{3}x+y=14 $