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Question
Find a if the sum of the slopes of lines represented by ax2 + 8xy + 5y2 = 0 is twice their product.
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Solution
Comparing the equation ax2 + 8xy + 5y2 = 0 with ax2 + 2hxy + by2 = 0,
we get, a = a, 2h = 8, b = 5
Let m1 and m2 be the slopes of the lines represented by ax2 + 8xy + 5y2 = 0.
∴ m1 + m2 = `(- 2"h")/"b" = -8/5`
and m1m2 = `"a"/"b" = "a"/5`
Now, (m1 + m2) = 2(m1m2)
`-8/5 = 2("a"/5)`
a = −4
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