Question

sketch and write the equation of a line on which the perpendicular from the origin is of the length 2 units and it makes an angle of 240 degree with the x - axis

Answer 1

Dear student
$$\begin{gathered} Innormalformequationofstriaghtlineisgivenby \\ x\cos \alpha +y\sin \alpha =p \\ where \\ p=lengthofnormalonthelinefromorigion. \\ \alpha =anglemadebynormalfrompositivesideofx-axis \\ Given:p=2and\alpha =240° \\ Equationoflinewillbe \\ x\cos 240°+y\sin 240°=2 \\ x\cos \left(180°+60°\right)+y\sin \left(180°+60°\right)=2 \\ -x\cos 60°-y\sin 60°=2 \\ -x\frac{1}{2}-y\frac{\sqrt{3}}{2}=2 \\ x+\sqrt{3}y=-4 \\ Regards \end{gathered}$$