Which of the following equation does not represent a pair of lines ?

Options

A. `x^(2)-x=0`
B. `xy-x=0`
C. `y^2-x+1=0`
D. `xy+x+y+1=0`

Answer

C

Explanation

`x^(2)-x=0`
`Rightarrow x(x-1)=0`
`Rightarrow x=0 and x=1`
Which represent a pair of lines.
`xy-x=0`
`Rightarrow x(y-1)=0`
`Rightarrow x=0, y=1`
Which represent a pair of lines.
`y^(2)-x+1=0`
`Rightarrow y^2=(x-1)`
Which represent a parabola.
Thus, it does not represent a pair of lines.
`xy+x+y+1=0`
`Rightarrow x(y+1)+(y+1)=0`
`Rightarrow (y+1)(x+1)=0`
`Rightarrow u=-1 and x=-1`
Which represent a pair of lines.