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Question
Find k, if one of the lines given by 6x2 + kxy + y2 = 0 is 2x + y = 0.
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Solution
The auxiliary equation of the lines represented by 6x2 + kxy + y2 = 0 is m2 + km + 6 = 0
Since one of the line is 2x + y = 0 whose slope is m = - 2.
∴ m = - 2 is the root of the auxiliary equation m2 + km + 6 = 0.
∴ (-2)2 + k(-2) + 6 = 0
∴ 4 - 2k + 6 = 0
∴ 2k = 10
∴ k = 5
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