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What does the equation $x^{3} y+x y^{3}-x y=0$ represent?
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Verified Answer
The correct answer is:
A pair of straight lines and a circle
$\begin{array}{ll}\text { Given equation } \\ x^{3} y+x y^{3}-x y & =0\end{array}$
$\Rightarrow x y\left(x^{2}+y^{2}\right)=x y$
$\Rightarrow x y\left(x^{2}+y^{2}-1\right)=0$
$\Rightarrow x^{2}+y^{2}=1, x y=0$
Above equations represent a pair of straight lines and a circle.
$\Rightarrow x y\left(x^{2}+y^{2}\right)=x y$
$\Rightarrow x y\left(x^{2}+y^{2}-1\right)=0$
$\Rightarrow x^{2}+y^{2}=1, x y=0$
Above equations represent a pair of straight lines and a circle.
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