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Find k, if one of the lines given by 6x^...

Find k, if one of the lines given by `6x^(2) + kxy + y^(2) = 0` is `2x + y = 0`.

Text Solution

Verified by Experts

The auxiliary equation of the lines represented by `6x^(2) + kxy + y^(2) = 0` is
`m^(2) + km + 6 = 0`.
Since one of the line is `2x + y = 0` whose slope is `m = -2`.
`therefore m = -2` is the root of the auxiliary equation `m^(2) + km + 6 = 0.`
`therefore (-2)^(2) +k(-2)+6 =0`
`therefore 4-2k + 6 = 0`
`therefore 2k = 10 therefore k = 5.`
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