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  • Find equation of the line through the point (0, 2) making an angle 2π/3 with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin.

Q : 14     . Find equation of the line through the point  (0,2)  making an angle \frac{2\pi }{3} with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin. 

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best_answer

We know that 
m = \tan \theta \\ m = \tan \frac{2\pi}{3} = -\sqrt3
Now, equation of line passing through point (0 , 2) and with slope -\sqrt3 is
(y-2)= -\sqrt3(x-0)\\ \sqrt3x+y-2=0
Therefore, equation of line is  \sqrt3x+y-2=0                 -(i)

Now, It is given that line crossing the y-axis at a distance of 2 units below the origin which means coordinates are  (0 ,-2)
This line is parallel to above line which means slope of both the lines are equal
Now, equation of line passing through point (0 , -2) and with slope -\sqrt3 is
(y-(-2))= -\sqrt3(x-0)\\ \sqrt3x+y+2=0
Therefore, equation of line is  \sqrt3x+y+2=0

Posted by

Gautam harsolia

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