Equation of graph and conic section

Question

If graph of the equation $x^3 +3x^2y +3xy^2 +y^3 -x^2+y^2=0$ comprises of a line and a conic section .

I am confused how can we find the equation of line and conic section separately .

Answer 1

Hint: Your equation is reducable to $$(x+y)^3=(x+y)(x-y)$$ $$(x+y)(x^2+y^2+2xy-x+y)=0$$

I gues you can seperate line and conic now