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Home » Which of the following equation does not represent a pair of lines ? A) B) C) D)
Which of the following equation does not represent a pair of lines ?
A) x^{2}-x=0
B) x y-x=0
C) y^{2}-x+1=0
D) x y+x+y+1=0
Maths
Which of the following equation does not represent a pair of lines ?
A) x^{2}-x=0
B) x y-x=0
C) y^{2}-x+1=0
D) x y+x+y+1=0

Solution:

Explanation:
(A) x^{2}-x=0
x^{2}-x=0
x(x-1)=0
\Longrightarrow \mathrm{x}=0 and \mathrm{x}=1
Therefore, it represents a pair of lines \mathrm{x}=0 and \mathrm{x}=1
(B) x y-x=0
\mathrm{x}(\mathrm{y}-1)=0
\Longrightarrow \mathrm{x}=0 and \mathrm{y}=1
Therefore, it represents a pair of lines \mathrm{x}=0 and \mathrm{y}=1
(C) y^{2}-x+1=0
\Longrightarrow \mathrm{y}^{2}=\mathrm{x}-1 which represents parabola
(D) x y+x+y+1=0
\begin{array}{l} \Longrightarrow \mathrm{x}(\mathrm{y}+1)+\mathrm{y}+1=0 \\ \Longrightarrow(\mathrm{y}+1)(\mathrm{x}+1)=0 \\ \Longrightarrow \mathrm{y}=-1 \text { and } \mathrm{x}=-1 \end{array}
Therefore, it represents a pair of lines \mathrm{x}=-1 and \mathrm{y}=-1
As a result, only (C) does not represents a pair of lines.

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