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  • Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120° with the positive direction of x-axis.

Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120° with the positive direction of x-axis.

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Given that length of the perpendicular from the origin is 4 units and line makes an angle with positive direction of x-axis 

  ∠BAX=120   

∠BA0=180-120=60

   ∠MAO=60  

 Now in triangle AMO ∠MAO+∠AOM+∠OMA=1800  

  600+θ+ 900=1800 

 θ=300   ∠AOM= 300 

 x cosθ+ysinθ=p 

 xcos 300+ysin300=4  

 x\left ( \frac{\sqrt{3}}{2} \right )+y\left ( \frac{\sqrt{1}}{2} \right )=4

\sqrt{3}x+y=8

 

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infoexpert22

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