The length of the perpendicular from the origin to a line is 7 and the perpendicular makes an angle of 150∘ with the positive direction of the x-axis. Find the equation of the line.
−√3x+y−14=0
Equation of the line in the normal form is
xcosα+ysinα=p
Here, give p = 7
α=150∘
cosα=cos150∘=cos(180∘−30∘)=−cos30∘=−√32
sinα=sin150∘=sin(180∘−30∘)=sin30∘=12
Equation of the line is
x(−√32)+7(12)=7
−√3x+y=14
−√3x+y−14=0