Question

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

• A. three real straight lines
• B. lines in which two of them are perpendicular to each other
• C. lines in which two of them are coincident
• D. none of these

Answer 1

Answer: (A), (B), (C)

lines in which two of them are perpendicular to each other
lines in which two of them are coincident
three real straight lines

By factorization, we get

$(x+y{)}^2(x-y)=0$

0 equations of lines are $x+y=0,x-y=0$

These two lines perpendicular.

and $x+y=0$ is coincident line.

Hence, options (A), (B) and (C) are correct.