Answer:
Option C
Explanation:
(a) $x^{2}-x=0$
$\Rightarrow$ x(x-1)=0
$\Rightarrow$ x=0 and x=1
which represent a pair of lines
(b) xy-x=0
$\Rightarrow$ x(y-1)=0
$\Rightarrow$ x=0, y=1
which represent a pair of lines
(c) $y^{2}-x+1$=0
$\Rightarrow$ $y^{2}=(x-1)$,
which represent a parabola
Thus , it does not represent a pair of lines
(d) xy+x+y+1=0
$\Rightarrow$ x(y-1)+(y+1)=0
$\Rightarrow$ (y+1)(x+1)=0
$\Rightarrow$ y=-1 and x=-1
which repesent a pair of lines
