Question

The equation $x^3-x^{2}y+x-y=0$ represents

• A. straight line
• B. a parabola and two lines
• C. a hyparabola and two lines
• D. a line and a circle

Answer 1

The correct option is A straight line

Given equation is $x^3-x^{2}y+x-y=0$
$\Rightarrow x^2(x-y)+(x-y)=0$
$\Rightarrow (x^2+1)(x-y)=0$
Since $x$ is real,
$x^2+1=0$ is not possible.
Hence, $x-y=0$ or $y=x$.
Thus the above expression represents a straight line.