Question

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

• A. $x^2-x=0$
• B. $xy-x=0$
• C. $y^2-x+1=0$
• D. $xy+x+y+1=0$

Answer 1

The correct option is C $y^2-x+1=0$

(A) $x^2-x=0$

$x^2-x=0$

$x(x-1)=0$

$⟹x=0$ and $x=1$

So, it represents a pair of lines $x=0$ and $x=1$

(B) $xy-x=0$

$x(y-1)=0$

$⟹x=0$ and $y=1$

So, it represents a pair of lines $x=0$ and $y=1$

(C) $y^2-x+1=0$

$⟹y^2=x-1$ which represents parabola

(D) $xy+x+y+1=0$

$⟹x(y+1)+y+1=0$

$⟹(y+1)(x+1)=0$

$⟹y=-1$ and $x=-1$

So, it represents a pair of lines $x=-1$ and $y=-1$.

Hence, only (C) does not represents a pair of lines.