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Question
Find the separate equation of the line represented by the following equation:
`3"x"^2 - 2sqrt3"xy" - 3"y"^2 = 0`
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Solution
`3"x"^2 - 2sqrt3"xy" - 3"y"^2 = 0`
∴ `3"x"^2 - 3sqrt3"xy" + sqrt3"xy" - 3"y"^2 = 0`
∴ `3"x"("x" - sqrt3"y") + sqrt3"y"("x" - sqrt3"y") = 0`
∴ `("x" - sqrt3"y")("3x" + sqrt3"y") = 0`
The separate equations of the lines are
∴ `"x" - sqrt3"y" = 0` and `"3x" + sqrt3"y" = 0`
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