The lines joining the origin to the points of intersection of  3x2+λxy−4x+1=0 and 12x+y−1=0 are at right angles for

Equation of the lines joining the origin to thepoints of intersection of the given lines is 3x2+λxy−4x(2x+y)+1⋅(2x+y)2=0(Making the equation of the pair of lines homogeneous withthe help of the equation of the line)⇒ x2−λxy−y2=0which are perpendicular for all values of l as the productof the slopes is -1