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Question

A straight line L at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of 60 with the line x+y=0. Then an equation of the line L is : 
  1. (3+1)x+(31)y=82
  2. (31)x+(3+1)y=82
  3. 3x+y=8
  4. x+3y=8


Solution

The correct option is B (31)x+(3+1)y=82


OA=p=4
x+y=0 makes an angle of 135 with the positive x-axis. 

Equation of the line L in perpendicular form is 
xcosθ+ysinθ=pxcos75+ysin75=px(3122)+y(3+122)=4x(31)+y(3+1)=82
 

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