The equations of the lines on which the perpendicular from the origin make 30 degree angle with x axis (in anticlockwise sense) and which form a triangle of area 50/√3 with axes,are

• x=√3+-10=0
• √3x+y+-10=0
• x+-√3y-10=0
• none of these

Angle made by the perpendicular with positive direction of x axis (1st quadrant) is 30.
Find the slope of line perpendicular to it. Correspondingly, find the angle it makes with x axis. Use trigonometry to get the relation between the intercept lengths of the 2 axes. Use this to find the area between the line and the intercepts it makes on the axes. Equate it to 50/√3 to get the value of intercepts. Write either intercept, slope intercept or two point form to get the equation.