Graph of the equation $x + y = x^{3} + y^{3}$ is the union of

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line and ellipse

line and parabola

line and hyperbola

line and a p at

answer is A.

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Detailed Solution

$\begin{array}{l} x + y - (x + y) (x^{2} - xy + y^{2}) = 0 \\ x + y = 0, x^{2} - xy + y^{2} - 1 = 0 \\ w h e r e ∆ \neq 0, h^{2} < a b s o i t r e p r e s e n t s e l l i p s e \end{array}$

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