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Question
Find the separate equation of the line represented by the following equation:
2x2 + 2xy - y2 = 0
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Solution
2x2 + 2xy - y2 = 0
The auxiliary equation is - m2 + 2m + 2 = 0
∴ m2 - 2m - 2 = 0
∴ m = `(2 +- sqrt((-2)^2 - 4(1)(-2)))/(2xx1)`
`= (2 +- sqrt(4 + 8))/2`
`= (2+- 2sqrt3)/2`
`= 1 +- sqrt3`
∴ m1 = 1 + `sqrt3` and m2 = 1 - `sqrt3` are the slopes of the lines.
∴ their separate equations are
y = m1x and y = m2x
i.e. y = `(1 + sqrt3)"x"` and y = `(1 - sqrt3)"x"`
i.e. `(sqrt3 + 1)"x" - "y" = 0` and `(sqrt3 - 1)"x" + "y" = 0`
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