Which among the following represents the combined equation of a pair of lines through point (1,0) and parallel to the lines represented by 2 x^2-x y-y^2=0 .

Step-by-step solution

Given line, 2 x^2-x y-y^2=0...(i) aligned 2 x^2-2 x y+x y-y^2 & =0 2 x(x-y)+y(x-y) & =0 (2 x+y)(x-y) & =0 aligned Since, we have given that combined equation of the pair is parallel to 2 x^2-x y-y^2=0 So, combined equation will be (2 x+y+k₁ ) (x-y+k₂ )=0 where k₁ and k₂ (ii) are constants. This equation satisfies (1, 0). array rrrl & (2 1+0+k₁ ) (1-0+k₂ ) & =0 & k₂=-1 and k₁ & =-2 array On putting the values of k₁ and k₂ in Eq. (ii) aligned (2 x+y-2)(x-y-1) & =0 2 x^2-x y-y^2-4 x+y+2 & =0 aligned