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Show that lines represented by x2 + 6xy + 9y2 = 0 are coincident.

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Comparing the equation x2 + 6xy + 9y2 = 0

with ax2 + 2hxy + by2 = 0, we get,

a = 1, 2h = 6, i.e. h = 3 and b = 9

Since h2 – ab = (3)2 – 1(9)

= 9 – 9 = 0, .

the lines represented by x2 + 6xy + 9y2 = 0 are coincident.

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