The equation of the line common to the pair of lines ( p ^2- q ^2 ) x ^2+ ( q ^2- r ^2 ) xy + ( r ^2- p ^2 ) y ^2=0 and (l- m ) x ^2+( m - n ) xy +( n -l) y ^2=0 is

Step-by-step solution

We have given equations of lines are: (p^2-q^2 ) x^2+ (q^2-r^2 ) x y+ (r^2-p^2 ) y^2=0 ...(i) And ( -m) x^2+(m-n) x y+(n- ) y^2=0 ...(ii) On comparing these two equations, we get p^2-q^2= -m, q^2-r^2=m-n & r^2-p^2=n- Note that points (1,1) and (0,0) satisfy the equation (i) & (ii). So, the line passing through (1,1) and (0,0) will be the common equation of line. (y-0)= 1-0 1-0 (x-0) y=x y-x=0