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Question
Show that the following equations represent a pair of line:
x2 + 7xy - 2y2 = 0
Solution
Comparing the equation x2 + 7xy - 2y2 = 0 with ax2 + 2hxy + by2 = 0, we get,
a = 1, 2h = 7 i,e, h = `7/2`, and b = - 2
∴ h2 - ab = `(7/2)^2` - 1 (- 2)
`= 49/4 + 2`
`= 57/4` i.e. 14.25 = 14 > 0
Since the equation x2 + 7xy - 2y2 = 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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