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

The correct option is B a straight line


$x^3-y{x}^2+x-y=0$
$\Rightarrow x^2(x-y)+1(x-y)=0$
$\Rightarrow (x^2+1)(x-y)=0$
We know that $(x^2+1)\ne 0$
Hence, $x-y=0$ is the only solution, which is a straight line.