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