The equation of a line which is parallel to the line common to the pair of lines given by 6x2−xy−12y2=0 and 15x2+14xy−8y2=0 and at a distance of 7 units from it is

We have 6x2−xy−12y2=0or (2x−3y)(3x+4y)=0_____(1)and 15x2+14xy−8y2=0or (5x−2y)(3x+4y)=0______(2)Equation of the line common to (1) and (2) is3x+4y=0______(3)Equation of any line parallel to (3) is 3x+4y=k Since its distance (3) is 7, we have |k32+42|=7or k=±35