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Question
If ax2 + 2hxy + by2 = 0 represents a pair of lines and h2 = ab ≠ 0 then find the ratio of their slopes.
Solution
h2 = ab
∴ h2 − ab = 0
∴ Lines are real and coincident.
Let m1 and m2 be the slope of lines represented by the equation ax2 + 2hxy + by2 = 0.
As the lines are real and coincident,
∴ m1 = m2
∴ `"m"_1/"m"_2` = 1
Their ratio is 1 : 1.
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