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Question
Show that the following equations represents a pair of line:
4x2 + 4xy + y2 = 0
Solution
Comparing the equation 4x2 + 4xy + y2 = 0 with ax2 + 2hxy + by2 = 0, we get,
a = 4, 2h = 4 i,e, h = 2, and b = 1
∴ h2 - ab = (2)2 - 4(1) = 4 - 4 = 0
Since the equation 4x2 + 4xy + y2 = 0 is a homogeneous equation of second degree and h2 - ab = 0, the given equation represents a pair of lines which are real and coincident.
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