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Double Ordinate of Ellipse

What locus ar...

Question

What locus are represented by the equation :
$x^{3} - y^{3} = 0.$

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Solution

$x^{3} - y^{3} = 0$
$y^{3} - x^{3} = 0 y^{3} = x^{3} \Rightarrow y = x$
Clearly this represents a straight line passing through the origin.

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