Question

The equation \(x^{3}-y x^{2}+x-y=0\) represents
(A) a hyperbola and two straight lines
(B) a straight line
(C) a parabola and two straight lines
(D) a straight line and a circle

Answer 1

Ans: (B)
 \(: x^{3}-y x^{2}+x-y=0 \Rightarrow x^{2}(x-y)+(x-y)=0\) \(\left(x^{2}+1\right)(x-y)=0\)
So only possibility is \(x=y\) as \(x^{2}+1 \neq 0\)
So it represents a straight line.