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 .
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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
The Dead Legend
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A line and circle through the origin. – Narasimham Apr 24 '17 at 03:21
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1@Narasimham the line is through origin. But the conic is certainly not a circle. – The Dead Legend Apr 24 '17 at 03:24
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Yes, it is a product of a parabola flaring down towards southeast passing through $(0,0),(1,0),(0,1)$ and line $x=y$ as axis. – Narasimham Apr 24 '17 at 03:56