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Question
Find k, if the sum of the slopes of the lines given by x2 + kxy − 3y2 = 0 is equal to their product.
Solution
Comparing the equation x2 + kxy − 3y2 = 0 with ax2 + 2hxy + by2 = 0, we get,
a = 1, 2h = k, b = −3
Let m1 and m2 be the slopes of the lines represented by x2 + kxy − 3y2 = 0.
∴ m1 + m2 = `(− 2"h")/"b" = (−"k")/(−3) = "k"/3`
m1m2 = `"a"/"b" = 1/(−3) = (−1)/3`
Now, m1 + m2 = m1m2 ...(Given)
∴ `"k"/3 = (−1)/3`
∴ k = −1.
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