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Find k, if the sum of slopes of the line...

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

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Comparing the equation `x^(2) + kxy - 3y^(2) = 0` with
`ax^(2) + 2hxy + by^(2) = 0, ` we get , `a = 1, 2h = k, b = -3`.
Let `M_(1) and m_(2)` be the slopes of the lines represented by `x^(2) -kxy - 3y^(2) = 0`.
`therefore m_(1) + m_(2) = (-2h)/(b) = -(k)/((-3)) = (k)/(3)`
and `m_(1)m_(2) = (a)/(b) = (1)/((-3)) = -(1)/(3)`.
NOw, `m_(1) + m_(2) = 2(m_(1)m_(2))" "`...(Given)
` therefore (k)/(3) = 2(-(1)/(3)) " " therefore k = -2.`
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