The value of ' (k ) ' for which the equation (x^2-4 x y-y^2+6 x+2 y+k=0 ) represents a pair of straight lines is equal to ........

Step-by-step solution

( aligned & x^2-4 x y-y^2+6 x+2 y+k=0 (i) & a=1,2 h=-4, b=-1,2 g=6,2 f=2, c=k aligned ) Eq. (i) Represents a pair of straight line ( aligned & =0 & a b c+2 f g h-a f^2-b g^2-c h^2=0 &( l )(-1)(k)+2(1)(3)(-2)-1(1)^2+1(3)^2-k(-2)^2=0 &-k-12-1+9-4 k=0 &-5 k-4=0 & k= -4 5 aligned ) Hence, option (c) is correct.