The equation `x^(3)+x^(2)y-xy^(2)-y^(3)=0` represents three straight lines passing through the origin such that

Options

A. two of them are coincident and two of them are perpendicular
B. two of them are coincident but no two are perpendicular
C. two of them are perpendicular but no two are coincident
D. None of the above

Answer

A

Explanation

We have , `x^3+x^2y-xy^2-y^3=0`
`rArr x^2(x+y)-y^2(x+y)=0`
`rArr (x+y)(x^2-y^2)=0`
`rArr (x+y)^2(x-y)=0`
`therefore x+y=0,x+y=0,x-y=0`
Clearly , two of the three lines represented by the given equation are coincident and two are perpendicular.