The straight line passing through (-1,1) and remaining parallel to the line common to the pairs of lines provided by 6 x^2-x y-12 y^2=0 and 15 x^2+14 x y-8 y^2=0 , is

Step-by-step solution

aligned & 6 x^2-x y-12 y^2=0 & 6 x^2-3 x y+8 x y-12 y^2=0 & (2 x-3 y)(3 x+4 y)=0 (i) & 15 x^2+14 x y-8 y^2=0 & 15 x^2+20 x y-6 x y-8 y^2=0 & (5 x-2 y)(3 x+4 y)=0 (ii) aligned Equation of common line from (i) and (ii) is aligned & 3 x +4 y =0 & y = -3 4 x slope ( m )= -3 4 aligned Equation of straight line passes through (-1,1) and parallel to 3 x +4 y =0 y-1= -3 4 (x+1) 3 x+4 y-=0