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Question
Find k, if the slope of one of the lines given by 3x2 - 4xy + ky2 = 0 is 1.
Solution
The auxiliary equation of the lines given by 3x2 - 4xy + ky2 = 0 is km2 - 4m + 3 = 0
Given, slope of one of the lines is 1.
∴ m = 1 is the root of the auxiliary equation km2 - 4m + 3 = 0
∴ k(1)2 - 4(1) + 3 = 0
∴ k - 4 + 3 = 0
∴ k = 1
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