If the lines represented by the equation 3y2−x2+23x−3=0 are rotated about the point (3,0) through an angle of 150, one in clockwise direction and the other in anticlockwise direction, so that they become perpendicular, then the equation of the pair of lines in the new position is

The given equation of the pair of straight lines can be rewritten as (3 y−x+3)(3 y+x−3)=0Their separate equations are 3y−x+3 =0 and 3y+x−3 =0or y=13x−1 and y=−13x+−1 or y=(tan 300)x−1 and y=(tan 1500)x+1After rotation through an angle of 150 as given in the question, the lines are (y−0)=tan 450(x−3) and (y−0)=tan 1350(x−3)or y=x−3 y=−x+3 Their combined equation is (y−x+3)(y+x−3)=0or y2−x2+23x−3=0