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Question
Show that the following equations represent a pair of line:
`"x"^2 - 2sqrt3"xy" - "y"^2 = 0`
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Solution
Comparing the equation `"x"^2 - 2sqrt3"xy" - "y"^2 = 0` with ax2 + 2hxy + by2 = 0, we get,
a = 1, 2h = `- 2sqrt3` i,e, h = `-sqrt3`, and b = - 1
∴ h2 - ab > 0
= `(-sqrt3)^2` - 1 (-1)
= 3 + 1 = 4 > 0
Since the equation `"x"^2 - 2sqrt3"xy" - "y"^2 = 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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