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Question
Find k, if the sum of the slopes of the lines given by 3x2 + kxy - y2 = 0 is zero.
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Solution
Comparing the equation 3x2 + kxy - y2 = 0 with ax2 + 2hxy + by2 = 0, we get,
a = 3, 2h = k, b = -1
Let m1 and m2 be the slopes of the lines represented by 3x2 + kxy - y2 = 0.
∴ m1 + m2 = `(- 2"h")/"b" = (-"k")/-1 = "k"`
Now, m1 + m2 = 0 ...(Given)
∴ k = 0
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