A line forms a triangle of area 543 sq-units with the coordinate axes. If the perpendicular drawn from the origin to the line makes an angle of 60° with the x-axis, then the equation the line is

Let p be the length of the perpendicular drawn from the origin to the required line. The perpendicular makes an angle of 60° with the x-axis. Putting a= 60° in xcos⁡α+ysin⁡α=p the equation of the line is xcos⁡60∘+ysin⁡60∘=por, x+3y=2p.This cuts the coordinate axes at A(2p,0) and B0,2p3It is given that           Area of △OAB=543 sq. units.⇒ 12(OA)(OB)=543⇒ 12×2p×2p3=543⇒p2=81⇒p=9Hence, the equation of the line is x+3y=18