Question

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

• A. three straight lines passing through origin
• B. three real straight lines
• C. three distinct points
• D. none of these

Answer 1

The correct option is D none of these

The given equation can be rewritten as $(x-y)(x^2+xy+2y^2)=0$

$x-y=0$ represents a straight line passing through origin.

But the equation $x^2+xy+2y^2=0$ represents two imaginary straight lines as

$h^2-ab=\frac{1}{4}-1.2=-\frac{7}{4}<0$

$\therefore$ the answer is option D