..What is the locus represented by the equation x^2-5xy+6y^2?
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Further x2− 5xy = 6y2 = x− 2yx− 3y The lines ...
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Factorising (x – 2y)(x – 3y) = 0
If x – 2y = 0 this is just a line of gradient a half through (0, 0)
If x – 3y = 0 this is just a line of gradient a third also through (0, 0)
The locus is these two intersecting lines.
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