Q.6 Find k , if the sum of the slopes of the lines represented by x² + kxy - 3y² = 0 is twice their product.

Answer: k = -2 Comparing with ax² + 2hxy + by² = 0 : a = 1,\ 2h = k,\ b = -3 . m₁ + m₂ = -2h/b = -k/-3 = k/3 , and m₁ m₂ = a/b = -1/3 . Given m₁ + m₂ = 2m₁m₂ : k/3 = -2/3 , so k = -2 .

Find \(k\), if the sum of the slopes of the lines represented by \(x^2 + kxy - 3y^2 = 0\) is twice their product.

Q.6 Find \(k\), if the sum of the slopes of the lines represented by \(x^2 + kxy - 3y^2 = 0\) is twice their product.

Doubtly Asked 28 Oct 2026 Board exam · March 2026 hsc 12th Save WhatsApp Report

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Answer: \(k = -2\)

Comparing with \(ax^2 + 2hxy + by^2 = 0\): \(a = 1,\ 2h = k,\ b = -3\).

\(m_1 + m_2 = -\dfrac{2h}{b} = -\dfrac{k}{-3} = \dfrac{k}{3}\), and \(m_1 m_2 = \dfrac{a}{b} = -\dfrac{1}{3}\).

Given \(m_1 + m_2 = 2m_1m_2\): \(\dfrac{k}{3} = -\dfrac{2}{3}\), so \(k = -2\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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Find \(k\), if the sum of the slopes of the lines represented by \(x^2 + kxy - 3y^2 = 0\) is twice their product.

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