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Question
Show that the following equations represents a pair of line:
x2 + 2xy - y2 = 0
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Solution
Comparing the equation x2 + 2xy - y2 = 0 with ax2 + 2hxy + by2 = 0, we get,
a = 1, 2h = 2 i,e, h = 1, and b = - 1
∴ h2 - ab = (1)2 - 1(- 1) = 1 + 1 = 2 > 0
Since the equation x2 + 2xy - 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 distinct.
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