Discussion Forum

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

Answer:

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