Correct Answer - A
Let `y=mx` be one of the lines represented by the given equation. Then, `y=mx` satisfies it.
`therefore" "lambda(1-3m^(2))+m^(3)-3m=0`
`rArr" "lambda=(3m-m^(3))/(1-3m^(2))`
`rArr" "tan phi=(3tantheta- tan^(3)theta)/(13tan^(2)theta)`, where `lambda= tan phi and m = tan theta`
`rArr" "tan phi=tan 3 theta`
`rArr" "3 theta=phi, pi + phi, 2pi + phi`
`rArr" "theta=(phi)/(3),(pi)/(3)+(phi)/(3),(2pi)/(3)+(phi)/(3)`
Hence, the given equation represents three lines passing through the origin such that they are equally inclined with one another.
