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Definition of Circle

What loci are...

Question

What loci are represented by the equation :
$x^{2} - x y = 0.$

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Solution

$x^{2} - x y = 0 x (x - y) = 0 x = 0, x = y$
So the given equation represents a homogeneous pair of straight lines passing through the origin.
One is the $y$ axis and other is the line $y = x$

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